Dimitra Karabali - Academia.edu (original) (raw)
Papers by Dimitra Karabali
arXiv (Cornell University), Oct 22, 2021
A parametrization of gauge fields on complex projective spaces of arbitrary dimension is given as... more A parametrization of gauge fields on complex projective spaces of arbitrary dimension is given as a generalization of the real two-dimensional case. Gauge transformations act homogeneously on the fields, facilitating a manifestly gauge-invariant analysis. Specializing to four dimensions, we consider the nature of the effective action due to chiral scalars interacting with the gauge fields. The key qualitatively significant terms include a possible gauge-invariant mass term and a finite four-dimensional Wess-Zumino-Witten (WZW) action. We comment on relating the mass term to lattice simulations as well as Schwinger-Dyson analyses, and also on relating the WZW action to the instanton liquid picture of QCD.
arXiv (Cornell University), Jul 29, 2023
An effective action for the bulk dynamics of quantum Hall effect in arbitrary even spatial dimens... more An effective action for the bulk dynamics of quantum Hall effect in arbitrary even spatial dimensions was obtained some time ago in terms of a Chern-Simons term associated with the Dolbeault index theorem. Here we explore further properties of this action, showing how electronic band structures can be incorporated, obtaining Hall currents and conductivity (for arbitrary dimensions) in terms of integrals of Chern classes for the bands. We also derive the expression for Hall viscosity from the effective action. Explicit formulae for the Hall viscosity are given for 2+1 and 4+1dimensions.
arXiv (Cornell University), Jun 20, 2022
We consider the volume of the gauge orbit space for gauge fields on four-dimensional complex proj... more We consider the volume of the gauge orbit space for gauge fields on four-dimensional complex projective space. The analysis uses a parametrization of gauge fields where gauge transformations act homogeneously on the fields, facilitating a manifestly gaugeinvariant analysis. The volume element contains a four-dimensional Wess-Zumino-Witten (WZW) action for a hermitian matrix-valued field. There is also a mass-like term for certain components of the gauge field. We discuss how the mass term could be related to results from lattice simulations as well as Schwinger-Dyson equations. We argue for a kinematic regime where the Yang-Mills theory can be approximated by the 4d-WZW theory. The result is suggestive of the instanton liquid picture of QCD. Further it is also indicative of the mechanism for confinement being similar to what happens in two dimensions.
Physical review, Oct 31, 2022
A parametrization of gauge fields on complex projective spaces of arbitrary dimension is given as... more A parametrization of gauge fields on complex projective spaces of arbitrary dimension is given as a generalization of the real two-dimensional case. Gauge transformations act homogeneously on the fields, facilitating a manifestly gauge-invariant analysis. Specializing to four dimensions, we consider the nature of the effective action due to chiral scalars interacting with the gauge fields. The key qualitatively significant terms include a possible gauge-invariant mass term and a finite four-dimensional Wess-Zumino-Witten (WZW) action. We comment on relating the mass term to lattice simulations as well as Schwinger-Dyson analyses and also on relating the WZW action to the instanton liquid picture of QCD.
Physical review, Oct 31, 2022
We consider the volume of the gauge orbit space for gauge fields on four-dimensional complex proj... more We consider the volume of the gauge orbit space for gauge fields on four-dimensional complex projective space. The analysis uses a parametrization of gauge fields where gauge transformations act homogeneously on the fields, facilitating a manifestly gauge-invariant analysis. The volume element contains a four-dimensional Wess-Zumino-Witten (WZW) action for a Hermitian matrix-valued field. There is also a masslike term for certain components of the gauge field. We discuss how the mass term could be related to results from lattice simulations as well as Schwinger-Dyson equations. We argue for a kinematic regime where the Yang-Mills theory can be approximated by the 4d-WZW theory. The result is suggestive of the instanton liquid picture of QCD. Further it is also indicative of the mechanism for confinement being similar to what happens in two dimensions.
Physical review, Sep 17, 2019
We calculate the pair production rates for spin-1 or vector particles on spaces of the form M ×R ... more We calculate the pair production rates for spin-1 or vector particles on spaces of the form M ×R 1,1 with M corresponding to R 2 (flat), S 2 (positive curvature) and H 2 (negative curvature), with and without a background (chromo)magnetic field on M. Beyond highlighting the effects of curvature and background magnetic field, this is particularly interesting since vector particles are known to suffer from the Nielsen-Olesen instability, which can dramatically increase pair production rates. The form of this instability for S 2 and H 2 is obtained. We also give a brief discussion of how our results relate to ideas about confinement in nonabelian theories.
![Research paper thumbnail of Erratum: Edges and diffractive effects in Casimir energies [Phys. Rev. D81, 125013 (2010)]](https://attachments.academia-assets.com/108931993/thumbnails/1.jpg)
](Physical review, Dec 7, 2011
Physical review, Feb 15, 1987
Fractional angular momentum in the O(3) nonlinear sigma model coupled to an Abelian gauge field w... more Fractional angular momentum in the O(3) nonlinear sigma model coupled to an Abelian gauge field with a topological mass is studied semiclassically. The results are suggestive of a phase transition in the fractionalization as the mass parameter is varied.
Physical review, Nov 20, 2018
We consider the Casimir effect in a gauge-invariant Hamiltonian formulation of non-Abelian gauge ... more We consider the Casimir effect in a gauge-invariant Hamiltonian formulation of non-Abelian gauge theories in (2 þ 1) dimensions, for an arbitrary gauge group. We show that the result is in good agreement with recent lattice simulations. We also argue that the Casimir effect may be viewed as a good probe of magnetic screening effects in (3 þ 1)-dimensional gauge theories at high temperatures.
Physical review, Dec 18, 2017
The entanglement entropy (EE) of gauge theories in three spacetime dimensions is analyzed using m... more The entanglement entropy (EE) of gauge theories in three spacetime dimensions is analyzed using manifestly gauge-invariant variables defined directly in the continuum. Specifically, we focus on the Maxwell, Maxwell-Chern-Simons (MCS), and nonabelian Yang-Mills theories. Special attention is paid to the analysis of edge modes and their contribution to EE. The contact term is derived without invoking the replica method and its physical origin is traced to the phase space volume measure for the edge modes. The topological contribution to the EE for the MCS case is calculated. For all the abelian cases, the EE presented in this paper agrees with known results in the literature. The EE for the nonabelian theory is computed in a gauge-invariant gaussian approximation, which incoprorates the dynamically generated mass gap. A formulation of the contact term for the nonabelian case is also presented.
Nuclear Physics B, Feb 1, 2008
We explore further the Hamiltonian formulation of Yang-Mills theory in 2+1 dimensions in terms of... more We explore further the Hamiltonian formulation of Yang-Mills theory in 2+1 dimensions in terms of gauge-invariant matrix variables. Coupling to scalar matter fields is discussed in terms of gauge-invariant fields. We analyze how the screening of adjoint (and other screenable) representations can arise in this formalism. A Schrödinger equation is then derived for the gluelump states which are the daughter states when an adjoint string breaks. A variational solution of this Schrödinger equation leads to an analytic estimate of the string-breaking energy which is within 8.8% of the latest lattice estimates.
Physical review, Jun 21, 2001
In earlier work we have given a Hamiltonian analysis of Yang-Mills theory in (2+1) dimensions sho... more In earlier work we have given a Hamiltonian analysis of Yang-Mills theory in (2+1) dimensions showing how a mass gap could arise. In this paper, generalizing and covariantizing from the mass term in the Hamiltonian analysis, we obtain two manifestly covariant and gauge-invariant mass terms which can be used in a resummation of standard perturbation theory to study properties of the mass gap.
Nuclear Physics B, 1986
The 2 + 1 dimensional 0(3) nonlinear sigma model with Hopf term of strength 0 is canonically quan... more The 2 + 1 dimensional 0(3) nonlinear sigma model with Hopf term of strength 0 is canonically quantized. The solitons of topological charge Q are found to have spin equal to (0/2~r)Q 2 modulo an integer. Collective coordinate quantization in the Q = 1 sector is described and there is a discussion of the current algebra of this model.
Nuclear Physics B, Oct 1, 1994
We show that a large class of incompressible quantum Hall states correspond to different represen... more We show that a large class of incompressible quantum Hall states correspond to different representations of the W ∞ algebra by explicit construction of the second quantized generators of the algebra in terms of fermion and vortex operators. These are parametrized by a set of integers which are related to the filling fraction. The class of states we consider includes multilayer Hall states and the states proposed by Jain to explain the hierarchical filling fractions. The corresponding second quantized order parameters are also given.
Nuclear Physics B, Apr 1, 1988
The massless spectrum of closed strings on group manifolds M a x H described by a Wess-Zumino-Wit... more The massless spectrum of closed strings on group manifolds M a x H described by a Wess-Zumino-Witten (WZW) action for the group H is studied. It is found that for certain groups H and central charge k of the associated Kac-Moody algebra, the massless spectrum does not coincide with the standard Kaluza-Klein spectrum. The nature of the extra, "accidental" massless states depends crucially on the multi-connectedness of H. In the presence of "accidental" gauge bosons, which requires multi-connected H, the gauge symmetry of the massless spectrum is enlarged to G L x GR, where H c G. A complete classification of "accidental" massless states is given for H = SU(2), SU(2)/Z2, SU(3) and SU(3)/Z 3 for every k.
International Journal of Modern Physics, Mar 30, 1991
Soliton operators of fractional spin and statistics are constructed using canonical quantization ... more Soliton operators of fractional spin and statistics are constructed using canonical quantization of the O(3) nonlinear sigma model with a topological Hopf action in 2+1 dimensions. The role of the Hopf term as the nontrivial holonomy of a flat connection in the configuration space is emphasized.
International Journal of Modern Physics, Nov 30, 1991
We present a collective field formalism for nonrelativistic fermions in one spatial dimension. A ... more We present a collective field formalism for nonrelativistic fermions in one spatial dimension. A bosonization technique is used to convert the quantum mechanical fermionic problem to a bosonic one, which is further described as a second quantized Schrödinger field theory. A formulation in terms of current and density variables gives rise to the collective field representation. Applications of our formalism to the D=1 Hermitian matrix model and the system of one-dimensional fermions in the presence of a weak electromagnetic field are discussed.
Physical review, Jan 16, 2008
In the first part of this paper, we present a set of simple arguments to show that the two-dimens... more In the first part of this paper, we present a set of simple arguments to show that the two-dimensional gauge anomaly and the (2 + 1)-dimensional Lorentz symmetry determine the leading Gaussian term in the vacuum wave function of (2 + 1)-dimensional Yang-Mills theory. This is to highlight the robustness of the wave function and its relative insensitivity to the choice of regularizations. We then comment on the correspondence with the explicit calculations done in earlier papers. We also make some comments on the nature of the gauge-invariant configuration space for Euclidean three-dimensional gauge fields (relevant to (3 + 1)-dimensional Yang-Mills theory).
Nuclear Physics B, Oct 1, 2005
Using a W N-gauge theory to describe electromagnetic interactions of spinless fermions in the low... more Using a W N-gauge theory to describe electromagnetic interactions of spinless fermions in the lowest Landau level, where the W N transformations are nonlinear realizations of U (1) gauge transformations, we construct the effective action describing electromagnetic interactions of a higher dimensional quantum Hall droplet. We also discuss how this is related to the Abelian Seiberg-Witten map. Explicit calculations are presented for the quantum Hall effect on CP k with U (1) background magnetic field. The bulk action is a Kähler-Chern-Simons term whose anomaly is cancelled by a boundary contribution so that gauge invariance is explicitly satisfied.
Nuclear Physics B, 2000
A Hamiltonian analysis of Yang-Mills (YM) theory in (2+1) dimensions with a level k Chern-Simons ... more A Hamiltonian analysis of Yang-Mills (YM) theory in (2+1) dimensions with a level k Chern-Simons term is carried out using a gauge invariant matrix parametrization of the potentials. The gauge boson states are constructed and the contribution of the dynamical mass gap to the gauge boson mass is obtained. Long distance properties of vacuum expectation values are related to a Euclidean two-dimensional YM theory coupled to k flavors of Dirac fermions in the fundamental representation. We also discuss the expectation value of the Wilson loop operator and give a comparison with previous results.
arXiv (Cornell University), Oct 22, 2021
A parametrization of gauge fields on complex projective spaces of arbitrary dimension is given as... more A parametrization of gauge fields on complex projective spaces of arbitrary dimension is given as a generalization of the real two-dimensional case. Gauge transformations act homogeneously on the fields, facilitating a manifestly gauge-invariant analysis. Specializing to four dimensions, we consider the nature of the effective action due to chiral scalars interacting with the gauge fields. The key qualitatively significant terms include a possible gauge-invariant mass term and a finite four-dimensional Wess-Zumino-Witten (WZW) action. We comment on relating the mass term to lattice simulations as well as Schwinger-Dyson analyses, and also on relating the WZW action to the instanton liquid picture of QCD.
arXiv (Cornell University), Jul 29, 2023
An effective action for the bulk dynamics of quantum Hall effect in arbitrary even spatial dimens... more An effective action for the bulk dynamics of quantum Hall effect in arbitrary even spatial dimensions was obtained some time ago in terms of a Chern-Simons term associated with the Dolbeault index theorem. Here we explore further properties of this action, showing how electronic band structures can be incorporated, obtaining Hall currents and conductivity (for arbitrary dimensions) in terms of integrals of Chern classes for the bands. We also derive the expression for Hall viscosity from the effective action. Explicit formulae for the Hall viscosity are given for 2+1 and 4+1dimensions.
arXiv (Cornell University), Jun 20, 2022
We consider the volume of the gauge orbit space for gauge fields on four-dimensional complex proj... more We consider the volume of the gauge orbit space for gauge fields on four-dimensional complex projective space. The analysis uses a parametrization of gauge fields where gauge transformations act homogeneously on the fields, facilitating a manifestly gaugeinvariant analysis. The volume element contains a four-dimensional Wess-Zumino-Witten (WZW) action for a hermitian matrix-valued field. There is also a mass-like term for certain components of the gauge field. We discuss how the mass term could be related to results from lattice simulations as well as Schwinger-Dyson equations. We argue for a kinematic regime where the Yang-Mills theory can be approximated by the 4d-WZW theory. The result is suggestive of the instanton liquid picture of QCD. Further it is also indicative of the mechanism for confinement being similar to what happens in two dimensions.
Physical review, Oct 31, 2022
A parametrization of gauge fields on complex projective spaces of arbitrary dimension is given as... more A parametrization of gauge fields on complex projective spaces of arbitrary dimension is given as a generalization of the real two-dimensional case. Gauge transformations act homogeneously on the fields, facilitating a manifestly gauge-invariant analysis. Specializing to four dimensions, we consider the nature of the effective action due to chiral scalars interacting with the gauge fields. The key qualitatively significant terms include a possible gauge-invariant mass term and a finite four-dimensional Wess-Zumino-Witten (WZW) action. We comment on relating the mass term to lattice simulations as well as Schwinger-Dyson analyses and also on relating the WZW action to the instanton liquid picture of QCD.
Physical review, Oct 31, 2022
We consider the volume of the gauge orbit space for gauge fields on four-dimensional complex proj... more We consider the volume of the gauge orbit space for gauge fields on four-dimensional complex projective space. The analysis uses a parametrization of gauge fields where gauge transformations act homogeneously on the fields, facilitating a manifestly gauge-invariant analysis. The volume element contains a four-dimensional Wess-Zumino-Witten (WZW) action for a Hermitian matrix-valued field. There is also a masslike term for certain components of the gauge field. We discuss how the mass term could be related to results from lattice simulations as well as Schwinger-Dyson equations. We argue for a kinematic regime where the Yang-Mills theory can be approximated by the 4d-WZW theory. The result is suggestive of the instanton liquid picture of QCD. Further it is also indicative of the mechanism for confinement being similar to what happens in two dimensions.
Physical review, Sep 17, 2019
We calculate the pair production rates for spin-1 or vector particles on spaces of the form M ×R ... more We calculate the pair production rates for spin-1 or vector particles on spaces of the form M ×R 1,1 with M corresponding to R 2 (flat), S 2 (positive curvature) and H 2 (negative curvature), with and without a background (chromo)magnetic field on M. Beyond highlighting the effects of curvature and background magnetic field, this is particularly interesting since vector particles are known to suffer from the Nielsen-Olesen instability, which can dramatically increase pair production rates. The form of this instability for S 2 and H 2 is obtained. We also give a brief discussion of how our results relate to ideas about confinement in nonabelian theories.
Physical review, Dec 7, 2011
Physical review, Feb 15, 1987
Fractional angular momentum in the O(3) nonlinear sigma model coupled to an Abelian gauge field w... more Fractional angular momentum in the O(3) nonlinear sigma model coupled to an Abelian gauge field with a topological mass is studied semiclassically. The results are suggestive of a phase transition in the fractionalization as the mass parameter is varied.
Physical review, Nov 20, 2018
We consider the Casimir effect in a gauge-invariant Hamiltonian formulation of non-Abelian gauge ... more We consider the Casimir effect in a gauge-invariant Hamiltonian formulation of non-Abelian gauge theories in (2 þ 1) dimensions, for an arbitrary gauge group. We show that the result is in good agreement with recent lattice simulations. We also argue that the Casimir effect may be viewed as a good probe of magnetic screening effects in (3 þ 1)-dimensional gauge theories at high temperatures.
Physical review, Dec 18, 2017
The entanglement entropy (EE) of gauge theories in three spacetime dimensions is analyzed using m... more The entanglement entropy (EE) of gauge theories in three spacetime dimensions is analyzed using manifestly gauge-invariant variables defined directly in the continuum. Specifically, we focus on the Maxwell, Maxwell-Chern-Simons (MCS), and nonabelian Yang-Mills theories. Special attention is paid to the analysis of edge modes and their contribution to EE. The contact term is derived without invoking the replica method and its physical origin is traced to the phase space volume measure for the edge modes. The topological contribution to the EE for the MCS case is calculated. For all the abelian cases, the EE presented in this paper agrees with known results in the literature. The EE for the nonabelian theory is computed in a gauge-invariant gaussian approximation, which incoprorates the dynamically generated mass gap. A formulation of the contact term for the nonabelian case is also presented.
Nuclear Physics B, Feb 1, 2008
We explore further the Hamiltonian formulation of Yang-Mills theory in 2+1 dimensions in terms of... more We explore further the Hamiltonian formulation of Yang-Mills theory in 2+1 dimensions in terms of gauge-invariant matrix variables. Coupling to scalar matter fields is discussed in terms of gauge-invariant fields. We analyze how the screening of adjoint (and other screenable) representations can arise in this formalism. A Schrödinger equation is then derived for the gluelump states which are the daughter states when an adjoint string breaks. A variational solution of this Schrödinger equation leads to an analytic estimate of the string-breaking energy which is within 8.8% of the latest lattice estimates.
Physical review, Jun 21, 2001
In earlier work we have given a Hamiltonian analysis of Yang-Mills theory in (2+1) dimensions sho... more In earlier work we have given a Hamiltonian analysis of Yang-Mills theory in (2+1) dimensions showing how a mass gap could arise. In this paper, generalizing and covariantizing from the mass term in the Hamiltonian analysis, we obtain two manifestly covariant and gauge-invariant mass terms which can be used in a resummation of standard perturbation theory to study properties of the mass gap.
Nuclear Physics B, 1986
The 2 + 1 dimensional 0(3) nonlinear sigma model with Hopf term of strength 0 is canonically quan... more The 2 + 1 dimensional 0(3) nonlinear sigma model with Hopf term of strength 0 is canonically quantized. The solitons of topological charge Q are found to have spin equal to (0/2~r)Q 2 modulo an integer. Collective coordinate quantization in the Q = 1 sector is described and there is a discussion of the current algebra of this model.
Nuclear Physics B, Oct 1, 1994
We show that a large class of incompressible quantum Hall states correspond to different represen... more We show that a large class of incompressible quantum Hall states correspond to different representations of the W ∞ algebra by explicit construction of the second quantized generators of the algebra in terms of fermion and vortex operators. These are parametrized by a set of integers which are related to the filling fraction. The class of states we consider includes multilayer Hall states and the states proposed by Jain to explain the hierarchical filling fractions. The corresponding second quantized order parameters are also given.
Nuclear Physics B, Apr 1, 1988
The massless spectrum of closed strings on group manifolds M a x H described by a Wess-Zumino-Wit... more The massless spectrum of closed strings on group manifolds M a x H described by a Wess-Zumino-Witten (WZW) action for the group H is studied. It is found that for certain groups H and central charge k of the associated Kac-Moody algebra, the massless spectrum does not coincide with the standard Kaluza-Klein spectrum. The nature of the extra, "accidental" massless states depends crucially on the multi-connectedness of H. In the presence of "accidental" gauge bosons, which requires multi-connected H, the gauge symmetry of the massless spectrum is enlarged to G L x GR, where H c G. A complete classification of "accidental" massless states is given for H = SU(2), SU(2)/Z2, SU(3) and SU(3)/Z 3 for every k.
International Journal of Modern Physics, Mar 30, 1991
Soliton operators of fractional spin and statistics are constructed using canonical quantization ... more Soliton operators of fractional spin and statistics are constructed using canonical quantization of the O(3) nonlinear sigma model with a topological Hopf action in 2+1 dimensions. The role of the Hopf term as the nontrivial holonomy of a flat connection in the configuration space is emphasized.
International Journal of Modern Physics, Nov 30, 1991
We present a collective field formalism for nonrelativistic fermions in one spatial dimension. A ... more We present a collective field formalism for nonrelativistic fermions in one spatial dimension. A bosonization technique is used to convert the quantum mechanical fermionic problem to a bosonic one, which is further described as a second quantized Schrödinger field theory. A formulation in terms of current and density variables gives rise to the collective field representation. Applications of our formalism to the D=1 Hermitian matrix model and the system of one-dimensional fermions in the presence of a weak electromagnetic field are discussed.
Physical review, Jan 16, 2008
In the first part of this paper, we present a set of simple arguments to show that the two-dimens... more In the first part of this paper, we present a set of simple arguments to show that the two-dimensional gauge anomaly and the (2 + 1)-dimensional Lorentz symmetry determine the leading Gaussian term in the vacuum wave function of (2 + 1)-dimensional Yang-Mills theory. This is to highlight the robustness of the wave function and its relative insensitivity to the choice of regularizations. We then comment on the correspondence with the explicit calculations done in earlier papers. We also make some comments on the nature of the gauge-invariant configuration space for Euclidean three-dimensional gauge fields (relevant to (3 + 1)-dimensional Yang-Mills theory).
Nuclear Physics B, Oct 1, 2005
Using a W N-gauge theory to describe electromagnetic interactions of spinless fermions in the low... more Using a W N-gauge theory to describe electromagnetic interactions of spinless fermions in the lowest Landau level, where the W N transformations are nonlinear realizations of U (1) gauge transformations, we construct the effective action describing electromagnetic interactions of a higher dimensional quantum Hall droplet. We also discuss how this is related to the Abelian Seiberg-Witten map. Explicit calculations are presented for the quantum Hall effect on CP k with U (1) background magnetic field. The bulk action is a Kähler-Chern-Simons term whose anomaly is cancelled by a boundary contribution so that gauge invariance is explicitly satisfied.
Nuclear Physics B, 2000
A Hamiltonian analysis of Yang-Mills (YM) theory in (2+1) dimensions with a level k Chern-Simons ... more A Hamiltonian analysis of Yang-Mills (YM) theory in (2+1) dimensions with a level k Chern-Simons term is carried out using a gauge invariant matrix parametrization of the potentials. The gauge boson states are constructed and the contribution of the dynamical mass gap to the gauge boson mass is obtained. Long distance properties of vacuum expectation values are related to a Euclidean two-dimensional YM theory coupled to k flavors of Dirac fermions in the fundamental representation. We also discuss the expectation value of the Wilson loop operator and give a comparison with previous results.