Pavan Kumar - Academia.edu (original) (raw)
Papers by Pavan Kumar
Journal of Mathematical Physics, 2019
The construction of fully (anti-)symmetric states with many particles, when the single particle s... more The construction of fully (anti-)symmetric states with many particles, when the single particle state carries multiple quantum numbers, is a problem that seems to have not been systematically addressed in the literature. A quintessential example is the construction of ground state baryon wave functions where the color singlet condition reduces the problem to just two (flavor and spin) quantum numbers. In this paper, we adddress the general problem and provide a formalism that applies to generic number of particles and generic number of quantum numbers. As an immediate result, we find a complete solution to the two quantum number case, from which the baryon wave function problem with arbitrary number of flavors follows. As a more elaborate illustration that reveals complications not visible in the two quantum number case, we present the complete class of states possible for a system of five fermionic particles with three quantum numbers each. Our formalism makes systematic use of pro...
Advances in Theoretical and Mathematical Physics, 2019
Building on a strategy introduced in arXiv:1706.05364, we present exact analytic expressions for ... more Building on a strategy introduced in arXiv:1706.05364, we present exact analytic expressions for all the singlet eigenstates and eigenvalues of the simplest non-linear (n " 2, d " 3) gauged Gurau-Witten tensor model. This solves the theory completely. The ground state eigenvalue is´2 ? 14 in suitable conventions. This matches the result obtained for the ground state energy in the ungauged model, via brute force diagonalization on a computer. We find that the leftover degeneracies in the gauged theory, are only partially accounted for by its known discrete symmetries, indicating the existence of previously unidentified "hidden" global symmetries in the system. We discuss the spectral form factor, the beginnings of chaos, and the distinction between theories with SOpnq and Opnq gaugings. Our results provide the complete analytic solution of a non-linear gauge theory in 0+1 dimensions, albeit for a specific value of N. A summary of the main results in this paper were presented in the companion letter arXiv:1802.02502.
Journal of High Energy Physics, 2017
We suggest that holographic tensor models related to SYK are viable candidates for exactly (ie., ... more We suggest that holographic tensor models related to SYK are viable candidates for exactly (ie., non-perturbatively in N) solvable holographic theories. The reason is that in these theories, the Hilbert space is a spinor representation, and the Hamiltonian (at least in some classes) can be arranged to commute with the Clifford level. This makes the theory solvable level by level. We demonstrate this for the specific case of the uncolored O(n) 3 tensor model with arbitrary even n, and reduce the question of determining the spectrum and eigenstates to an algebraic equation relating Young tableaux. Solving this reduced problem is conceptually trivial and amounts to matching the representations on either side, as we demonstrate explicitly at low levels. At high levels, representations become bigger, but should still be tractable. None of our arguments require any supersymmetry.
Journal of High Energy Physics, 2019
We show that a natural spinor-helicity formalism that can describe massive scattering amplitudes ... more We show that a natural spinor-helicity formalism that can describe massive scattering amplitudes exists in D = 6 dimensions. This is arranged by having helicity spinors carry an index in the Dirac spinor 4 of the massive little group, SO(5) ∼ Sp(4). In the high energy limit, two separate kinds of massless helicity spinors emerge as required for consistency with arXiv:0902.0981, with indices in the two SU(2)’s of the massless little group SO(4). The tensors of 4 lead to particles with arbitrary spin, and using these and demanding consistent factorization, we can fix 3− and 4-point tree amplitudes of arbitrary masses and spins: we provide examples. We discuss the high energy limit of scattering amplitudes and the Higgs mechanism in this language, and make some preliminary observations about massive BCFW recursion.
Journal of High Energy Physics, 2018
We contrast some aspects of various SYK-like models with large-N melonic behavior. First, we note... more We contrast some aspects of various SYK-like models with large-N melonic behavior. First, we note that ungauged tensor models can exhibit symmetry breaking, even though these are 0+1 dimensional theories. Related to this, we show that when gauged, some of them admit no singlets, and are anomalous. The uncolored Majorana tensor model with even N is a simple case where gauge singlets can exist in the spectrum. We outline a strategy for solving for the singlet spectrum, taking advantage of the results in arXiv:1706.05364, and reproduce the singlet states expected in N = 2. In the second part of the paper, we contrast the random matrix aspects of some ungauged tensor models, the original SYK model, and a model due to Gross and Rosenhaus. The latter, even though disorder averaged, shows parallels with the Gurau-Witten model. In particular, the two models fall into identical Andreev ensembles as a function of N. In an appendix, we contrast the (expected) spectra of AdS 2 quantum gravity, SYK and SYK-like tensor models, and the zeros of the Riemann Zeta function.
Physical review letters, Jan 18, 2018
Gauged tensor models are a class of strongly coupled quantum mechanical theories. We present the ... more Gauged tensor models are a class of strongly coupled quantum mechanical theories. We present the exact analytic solution of a specific example of such a theory: namely, the smallest colored tensor model due to Gurau and Witten that exhibits nonlinearities. We find explicit analytic expressions for the eigenvalues and eigenstates, and the former agree precisely with previous numerical results on (a subset of) eigenvalues of the ungauged theory. The physics of the spectrum, despite the smallness of N, exhibits rudimentary signatures of chaos. This Letter is a summary of our main results: the technical details will appear in companion paper [C. Krishnan and K. V. Pavan Kumar, Complete solution of a gauged tensor model, arXiv:1804.10103].
Journal of High Energy Physics, 2017
We further explore the connection between holographic O(n) tensor models and random matrices. Fir... more We further explore the connection between holographic O(n) tensor models and random matrices. First, we consider the simplest non-trivial uncolored tensor model and show that the results for the density of states, level spacing and spectral form factor are qualitatively identical to the colored case studied in arXiv:1612.06330. We also explain an overall 16-fold degeneracy by identifying various symmetries, some of which were unavailable in SYK and the colored models. Secondly, and perhaps more interestingly, we systematically identify the Spectral Mirror Symmetry and the Time-Reversal Symmetry of both the colored and uncolored models for all values of n, and use them to identify the Andreev ensembles that control their random matrix behavior. We find that the ensembles that arise exhibit a refined version of Bott periodicity in n.
Journal of High Energy Physics, 2016
We define a (semi-classical) path integral for gravity with Neumann boundary conditions in D dime... more We define a (semi-classical) path integral for gravity with Neumann boundary conditions in D dimensions, and show how to relate this new partition function to the usual picture of Euclidean quantum gravity. We also write down the action in ADM Hamiltonian formulation and use it to reproduce the entropy of black holes and cosmological horizons. A comparison between the (background-subtracted) covariant and Hamiltonian ways of semi-classically evaluating this path integral in flat space reproduces the generalized Smarr formula and the first law. This "Neumann ensemble" perspective on gravitational thermodynamics is parallel to the canonical (Dirichlet) ensemble of Gibbons-Hawking and the microcanonical approach of Brown-York.
Methods in molecular biology (Clifton, N.J.), 2013
Here, we describe a series of methods suitable for the measurement of cytosolic ion concentration... more Here, we describe a series of methods suitable for the measurement of cytosolic ion concentrations in living plant cells using ion selective dyes. We describe procedures for the use of SBFI for the measurement of Na(+) in live cells. The resulting material is suitable for most standard cell biology procedures.
Journal of Biological Chemistry, 2007
Stress responses in both plants and yeast utilize calcium-mediated signaling. A yeast strain, K61... more Stress responses in both plants and yeast utilize calcium-mediated signaling. A yeast strain, K616, which lacks Ca 2؉ pumps, requires micromolar Ca 2؉ for growth. In medium containing 100 M Ca 2؉ , K616 can withstand osmotic stress (750 mM sorbitol) and ionic stress (300 mM KCl) but not hypersodic stress (300 mM NaCl). Heterologous expression of the endoplasmic reticulum-located Arabidopsis thaliana Ca 2؉-ATPase, ACA2, permits K616 to grow under NaCl stress even in Ca 2؉-depleted medium. All stresses tested generated transient elevation of cytosolic Ca 2؉ in wild type yeast, K601, whereas NaCl alone induced prolonged elevation of cytosolic Ca 2؉ in K616. Both the Ca 2؉ transient and survival of cultures subjected to NaCl stress was similar for the ACA2 transformant and K601. However, whereas K601 maintained low cytosolic Na ؉ predominantly by pumping it out across the plasma membrane, the transformant sequestered Na ؉ in internal organelles. This sequestration requires the presence of an endomembrane Na ؉ /H ؉-antiporter, NHX1, which does not play a significant role in salt tolerance of wild type yeast except at acidic pH. Transcript levels of the plasma membrane Na ؉-ATPase, ENA1, were strongly induced only in K601, whereas NHX1 was strongly induced in both K601 and the ACA2 transformant. The calmodulin kinase inhibitor KN62 significantly reduced the salt tolerance of the ACA2 transformant and the transcriptional induction of NHX1. Thus, the heterologous expression of a plant endomembrane Ca 2؉ pump results in the rapid depletion of cytosolic Ca 2؉ and the activation of an alternate mechanism for surviving saline stress.
Journal of Mathematical Physics, 2019
The construction of fully (anti-)symmetric states with many particles, when the single particle s... more The construction of fully (anti-)symmetric states with many particles, when the single particle state carries multiple quantum numbers, is a problem that seems to have not been systematically addressed in the literature. A quintessential example is the construction of ground state baryon wave functions where the color singlet condition reduces the problem to just two (flavor and spin) quantum numbers. In this paper, we adddress the general problem and provide a formalism that applies to generic number of particles and generic number of quantum numbers. As an immediate result, we find a complete solution to the two quantum number case, from which the baryon wave function problem with arbitrary number of flavors follows. As a more elaborate illustration that reveals complications not visible in the two quantum number case, we present the complete class of states possible for a system of five fermionic particles with three quantum numbers each. Our formalism makes systematic use of pro...
Advances in Theoretical and Mathematical Physics, 2019
Building on a strategy introduced in arXiv:1706.05364, we present exact analytic expressions for ... more Building on a strategy introduced in arXiv:1706.05364, we present exact analytic expressions for all the singlet eigenstates and eigenvalues of the simplest non-linear (n " 2, d " 3) gauged Gurau-Witten tensor model. This solves the theory completely. The ground state eigenvalue is´2 ? 14 in suitable conventions. This matches the result obtained for the ground state energy in the ungauged model, via brute force diagonalization on a computer. We find that the leftover degeneracies in the gauged theory, are only partially accounted for by its known discrete symmetries, indicating the existence of previously unidentified "hidden" global symmetries in the system. We discuss the spectral form factor, the beginnings of chaos, and the distinction between theories with SOpnq and Opnq gaugings. Our results provide the complete analytic solution of a non-linear gauge theory in 0+1 dimensions, albeit for a specific value of N. A summary of the main results in this paper were presented in the companion letter arXiv:1802.02502.
Journal of High Energy Physics, 2017
We suggest that holographic tensor models related to SYK are viable candidates for exactly (ie., ... more We suggest that holographic tensor models related to SYK are viable candidates for exactly (ie., non-perturbatively in N) solvable holographic theories. The reason is that in these theories, the Hilbert space is a spinor representation, and the Hamiltonian (at least in some classes) can be arranged to commute with the Clifford level. This makes the theory solvable level by level. We demonstrate this for the specific case of the uncolored O(n) 3 tensor model with arbitrary even n, and reduce the question of determining the spectrum and eigenstates to an algebraic equation relating Young tableaux. Solving this reduced problem is conceptually trivial and amounts to matching the representations on either side, as we demonstrate explicitly at low levels. At high levels, representations become bigger, but should still be tractable. None of our arguments require any supersymmetry.
Journal of High Energy Physics, 2019
We show that a natural spinor-helicity formalism that can describe massive scattering amplitudes ... more We show that a natural spinor-helicity formalism that can describe massive scattering amplitudes exists in D = 6 dimensions. This is arranged by having helicity spinors carry an index in the Dirac spinor 4 of the massive little group, SO(5) ∼ Sp(4). In the high energy limit, two separate kinds of massless helicity spinors emerge as required for consistency with arXiv:0902.0981, with indices in the two SU(2)’s of the massless little group SO(4). The tensors of 4 lead to particles with arbitrary spin, and using these and demanding consistent factorization, we can fix 3− and 4-point tree amplitudes of arbitrary masses and spins: we provide examples. We discuss the high energy limit of scattering amplitudes and the Higgs mechanism in this language, and make some preliminary observations about massive BCFW recursion.
Journal of High Energy Physics, 2018
We contrast some aspects of various SYK-like models with large-N melonic behavior. First, we note... more We contrast some aspects of various SYK-like models with large-N melonic behavior. First, we note that ungauged tensor models can exhibit symmetry breaking, even though these are 0+1 dimensional theories. Related to this, we show that when gauged, some of them admit no singlets, and are anomalous. The uncolored Majorana tensor model with even N is a simple case where gauge singlets can exist in the spectrum. We outline a strategy for solving for the singlet spectrum, taking advantage of the results in arXiv:1706.05364, and reproduce the singlet states expected in N = 2. In the second part of the paper, we contrast the random matrix aspects of some ungauged tensor models, the original SYK model, and a model due to Gross and Rosenhaus. The latter, even though disorder averaged, shows parallels with the Gurau-Witten model. In particular, the two models fall into identical Andreev ensembles as a function of N. In an appendix, we contrast the (expected) spectra of AdS 2 quantum gravity, SYK and SYK-like tensor models, and the zeros of the Riemann Zeta function.
Physical review letters, Jan 18, 2018
Gauged tensor models are a class of strongly coupled quantum mechanical theories. We present the ... more Gauged tensor models are a class of strongly coupled quantum mechanical theories. We present the exact analytic solution of a specific example of such a theory: namely, the smallest colored tensor model due to Gurau and Witten that exhibits nonlinearities. We find explicit analytic expressions for the eigenvalues and eigenstates, and the former agree precisely with previous numerical results on (a subset of) eigenvalues of the ungauged theory. The physics of the spectrum, despite the smallness of N, exhibits rudimentary signatures of chaos. This Letter is a summary of our main results: the technical details will appear in companion paper [C. Krishnan and K. V. Pavan Kumar, Complete solution of a gauged tensor model, arXiv:1804.10103].
Journal of High Energy Physics, 2017
We further explore the connection between holographic O(n) tensor models and random matrices. Fir... more We further explore the connection between holographic O(n) tensor models and random matrices. First, we consider the simplest non-trivial uncolored tensor model and show that the results for the density of states, level spacing and spectral form factor are qualitatively identical to the colored case studied in arXiv:1612.06330. We also explain an overall 16-fold degeneracy by identifying various symmetries, some of which were unavailable in SYK and the colored models. Secondly, and perhaps more interestingly, we systematically identify the Spectral Mirror Symmetry and the Time-Reversal Symmetry of both the colored and uncolored models for all values of n, and use them to identify the Andreev ensembles that control their random matrix behavior. We find that the ensembles that arise exhibit a refined version of Bott periodicity in n.
Journal of High Energy Physics, 2016
We define a (semi-classical) path integral for gravity with Neumann boundary conditions in D dime... more We define a (semi-classical) path integral for gravity with Neumann boundary conditions in D dimensions, and show how to relate this new partition function to the usual picture of Euclidean quantum gravity. We also write down the action in ADM Hamiltonian formulation and use it to reproduce the entropy of black holes and cosmological horizons. A comparison between the (background-subtracted) covariant and Hamiltonian ways of semi-classically evaluating this path integral in flat space reproduces the generalized Smarr formula and the first law. This "Neumann ensemble" perspective on gravitational thermodynamics is parallel to the canonical (Dirichlet) ensemble of Gibbons-Hawking and the microcanonical approach of Brown-York.
Methods in molecular biology (Clifton, N.J.), 2013
Here, we describe a series of methods suitable for the measurement of cytosolic ion concentration... more Here, we describe a series of methods suitable for the measurement of cytosolic ion concentrations in living plant cells using ion selective dyes. We describe procedures for the use of SBFI for the measurement of Na(+) in live cells. The resulting material is suitable for most standard cell biology procedures.
Journal of Biological Chemistry, 2007
Stress responses in both plants and yeast utilize calcium-mediated signaling. A yeast strain, K61... more Stress responses in both plants and yeast utilize calcium-mediated signaling. A yeast strain, K616, which lacks Ca 2؉ pumps, requires micromolar Ca 2؉ for growth. In medium containing 100 M Ca 2؉ , K616 can withstand osmotic stress (750 mM sorbitol) and ionic stress (300 mM KCl) but not hypersodic stress (300 mM NaCl). Heterologous expression of the endoplasmic reticulum-located Arabidopsis thaliana Ca 2؉-ATPase, ACA2, permits K616 to grow under NaCl stress even in Ca 2؉-depleted medium. All stresses tested generated transient elevation of cytosolic Ca 2؉ in wild type yeast, K601, whereas NaCl alone induced prolonged elevation of cytosolic Ca 2؉ in K616. Both the Ca 2؉ transient and survival of cultures subjected to NaCl stress was similar for the ACA2 transformant and K601. However, whereas K601 maintained low cytosolic Na ؉ predominantly by pumping it out across the plasma membrane, the transformant sequestered Na ؉ in internal organelles. This sequestration requires the presence of an endomembrane Na ؉ /H ؉-antiporter, NHX1, which does not play a significant role in salt tolerance of wild type yeast except at acidic pH. Transcript levels of the plasma membrane Na ؉-ATPase, ENA1, were strongly induced only in K601, whereas NHX1 was strongly induced in both K601 and the ACA2 transformant. The calmodulin kinase inhibitor KN62 significantly reduced the salt tolerance of the ACA2 transformant and the transcriptional induction of NHX1. Thus, the heterologous expression of a plant endomembrane Ca 2؉ pump results in the rapid depletion of cytosolic Ca 2؉ and the activation of an alternate mechanism for surviving saline stress.