Carmelo Martín - Academia.edu (original) (raw)

Papers by Carmelo Martín

Research paper thumbnail of A note on unimodular N=1, d=4 AdS supergravity

Journal of Cosmology and Astroparticle Physics

Research paper thumbnail of Off-shell unimodular N = 1, d = 4 supergravity

Journal of High Energy Physics

We formulate a unimodular N = 1, d = 4 supergravity theory off shell. We see that the infinitesim... more We formulate a unimodular N = 1, d = 4 supergravity theory off shell. We see that the infinitesimal Grassmann parameters defining the unimodular supergravity transformations are constrained and show that the conmutator of two infinitesinal unimodular supergravity transformations closes on transverse diffeomorphisms, Lorentz transformations and unimodular supergravity transformations. Along the way, we also show that the linearized theory is a supersymmetric theory of gravitons and gravitinos. We see that de Sitter and anti-de Sitter spacetimes are non-supersymmetric vacua of our unimodular supergravity theory.

Research paper thumbnail of Quantum noncommutative ABJM theory: first steps

Journal of High Energy Physics

We introduce ABJM quantum field theory in the noncommutative spacetime by using the component for... more We introduce ABJM quantum field theory in the noncommutative spacetime by using the component formalism and show that it is mathcalN\mathcal{N}mathcalN N = 6 supersymmetric. For the U(1) κ × U(1)−κ case, we compute all one-loop 1PI two and three point functions in the Landau gauge and show that they are UV finite and have well-defined commutative limits θ μν → 0, corresponding exactly to the 1PI functions of the ordinary ABJM field theory. This result also holds for all one-loop functions which are UV finite by power counting. It seems that the noncommutative quantum ABJM field theory is free from the noncommutative IR instabilities.

Research paper thumbnail of Unimodular gravity and the lepton anomalous magnetic moment at one-loop

Journal of Cosmology and Astroparticle Physics

We work out the one-loop contribution to the lepton anomalous magnetic moment coming from Unimodu... more We work out the one-loop contribution to the lepton anomalous magnetic moment coming from Unimodular Gravity. We use Dimensional Regularization and Dimensional Reduction to carry out the computations. In either case, we find that Unimodular Gravity gives rise to the same one-loop correction as that of General Relativity.

Research paper thumbnail of Equivalence of quantum field theories related by theθ-exact Seiberg-Witten map

Physical Review D

The equivalence of the noncommutative U(N) quantum field theories related by the θ-exact Seiberg-... more The equivalence of the noncommutative U(N) quantum field theories related by the θ-exact Seiberg-Witten maps is, in this paper, proven to all orders in the perturbation theory with respect to the coupling constant. We show that this holds for super Yang-Mills theories with N = 0, 1, 2, 4 supersymmetry. A direct check of this equivalence relation is performed by computing the one-loop quantum corrections to the quadratic part of the effective action in the noncommutative U(1) gauge theory with N = 0, 1, 2, 4 supersymmetry.

Research paper thumbnail of Quantum duality under the θ-exact Seiberg-Witten map

Journal of High Energy Physics

We show that in the perturbative regime defined by the coupling constant, the θ-exact Seiberg-Wit... more We show that in the perturbative regime defined by the coupling constant, the θ-exact Seiberg-Witten map applied to the noncommutative U(N) Yang-Mills-with or without Supersymmetry-gives an ordinary gauge theory which is, at the quantum level, dual to the former. We do so by using the on-shell DeWitt effective action and dimensional regularization. We explicitly compute the one-loop two-point function contribution to the on-shell DeWitt effective action of the ordinary U(1) theory furnished by the θ-exact Seiberg-Witten map. We find that the non-local UV divergences found in the propagator in the Feynman gauge all but disappear, so that they are not physically relevant. We also show that the quadratic noncommutative IR divergences are gauge-fixing independent and go away in the Supersymmetric version of the U(1) theory.

Research paper thumbnail of Unimodular trees versus Einstein trees

The European Physical Journal C, 2016

The maximally helicity violating tree-level scattering amplitudes involving three, four or five g... more The maximally helicity violating tree-level scattering amplitudes involving three, four or five gravitons are worked out in Unimodular Gravity. They are found to coincide with the corresponding amplitudes in General Relativity. This a remarkable result, insofar as both the propagators and the vertices are quite different in the two theories.

Research paper thumbnail of U(1){sub A} anomaly in noncommutative SU(N) theories

Phys Rev D, 2005

We work out the one-loop U(1){sub A} anomaly for noncommutative SU(N) gauge theories up to second... more We work out the one-loop U(1){sub A} anomaly for noncommutative SU(N) gauge theories up to second order in the noncommutative parameter θ{sup μ}{sup ν}. We set θ{sup 0i}=0 and conclude that there is no breaking of the classical U(1){sub A} symmetry of the theory coming from the contributions that are either linear or quadratic in θ{sup μ}{sup ν}. Of course, the ordinary anomalous contributions will be still with us. We also show that the one-loop conservation of the nonsinglet currents holds at least up to second order in θ{sup μ}{sup ν}. We adapt our results to noncommutative gauge theories with SO(N) and U(1) gauge groups.

Research paper thumbnail of The light-cone gauge, Chern-Simons theory and topologically massive Yang-Mills theory

In this paper, we complete our study of one-loop perturbative Chern-Simons theoiy in the light-co... more In this paper, we complete our study of one-loop perturbative Chern-Simons theoiy in the light-cone gauge n A" = 0, n 2 = 0. Using a gauge-invariant regularization procedure, which defines Chern-Simons theory as the large-mass limit of a topologically massive field theory, we evaluate the three-point function I',~'(p 1, P2, p3) to one loop. The spurious poles of (q. nY

Research paper thumbnail of Note on the gauge symmetries of unimodular gravity

Physical Review D, 2016

The symmetries of Unimodular Gravity are clarified somewhat.

Research paper thumbnail of Conformal dilaton gravity: Classical noninvariance gives rise to quantum invariance

Physical Review D, 2016

When quantizing Conformal Dilaton Gravity there is a conformal anomaly which starts at two loop o... more When quantizing Conformal Dilaton Gravity there is a conformal anomaly which starts at two loop order. This anomaly stems from evanescent operators on the divergent parts of the effective action. The general form of the finite counterterm which is necessary in order to insure cancellation of the Weyl anomaly to every order in perturbation theory has been determined using only conformal invariance. Those finite counterterms do not have any inverse power of any mass scale in front of them (precisely because of conformal invariance) and then they are not negligible in the low energy deep infrared limit. The general form of the ensuing modifications to the scalar field equation of motion has been determined and some physical consequences extracted.

Research paper thumbnail of Super Yang-Mills and θ-exact Seiberg-Witten map: absence of quadratic noncommutative IR divergences

Journal of High Energy Physics, 2016

We compute the one-loop 1PI contributions to all the propagators of the noncommutative (NC) N = 1... more We compute the one-loop 1PI contributions to all the propagators of the noncommutative (NC) N = 1, 2, 4 super Yang-Mills (SYM) U(1) theories defined by the means of the θ-exact Seiberg-Witten (SW) map in the Wess-Zumino gauge. Then we extract the UV divergent contributions and the noncommutative IR divergences. We show that all the quadratic noncommutative IR divergences add up to zero in each propagator.

Research paper thumbnail of Does Stochastic Analytic Regularization Provide Quantum Field Theories?

Ijmpa, 1992

We analyze whether the so-called method of stochastic analytic regularization is suitable as an i... more We analyze whether the so-called method of stochastic analytic regularization is suitable as an intermediate step for constructing perturbative renormalized quantum field theories. We choose a λϕ3 in six dimensions to prove that this regularization method does not in general provide a quantum field theory. This result seems to apply to any field theory with a quadratically UV-divergent stochastic two-point function, for instance λϕ4 and gauge theories in four dimensions.

Research paper thumbnail of Noncommutative ?? = 1 super Yang-Mills, the Seiberg-Witten map and UV divergences

J High Energy Phys, 2009

Page 1. Noncommutative = 1 super Yang-Mills, the Seiberg-Witten map and UV divergences This artic... more Page 1. Noncommutative = 1 super Yang-Mills, the Seiberg-Witten map and UV divergences This article has been downloaded from IOPscience. ... Noncommutative A = 1 super Yang-Mills, the Seiberg-Witten map and UV divergences CP Mart´ına and C. Tamaritb ...

Research paper thumbnail of Iñaki Gabilondo, ciudadano en Gran Vía: la aventura de 30 años de radio

Research paper thumbnail of Quantum corrections to unimodular gravity

Journal of High Energy Physics, 2015

The problem of the cosmological constant appears in a new light in Unimodular Gravity. In particu... more The problem of the cosmological constant appears in a new light in Unimodular Gravity. In particular, the zero momentum piece of the potential (that is, the constant piece independent of the matter fields) does not automatically produce a cosmological constant proportional to it. The aim of this paper is to give some details on a calculation showing that quantum corrections do not renormalize the classical value of this observable.

Research paper thumbnail of Parameter restrictions in a non-commutative geometry model do not survive standard quantum corrections

Physics Letters B, 1993

We have investigated the standard one-loop quantum corrections for a particularly simple non-comm... more We have investigated the standard one-loop quantum corrections for a particularly simple non-commutative geometry model containing fermions interacting with a unique abelian gauge field and a unique scalar through Yukawa couplings. In this model there are certain relations among the different coupling constants quite similar to the ones appearing in the Connes-Lott version of the standard model. We find that it is not possible to implement those relations in a renormalization-group invariant way.

Research paper thumbnail of Critical exponents at the three-loop level from stochastic continuum regularization

Research paper thumbnail of Renormalisability of noncommutative GUT inspired field theories with anomaly safe groups

Journal of High Energy Physics, 2009

We consider noncommutative GUT inspired field theories formulated within the enveloping-algebra f... more We consider noncommutative GUT inspired field theories formulated within the enveloping-algebra formalism for anomaly safe compact simple gauge groups. Our theories have only gauge fields and fermions, and we compute the UV divergent part of the one-loop background-field effective action involving two fermionic fields at first order in the noncommutativity parameter θ. We show that, if the second-degree Casimir has the same value for all the irreps furnished by the fermionic multiplets of the model, then, that UV divergent part can be renormalised by carrying out multiplicative renormalisations of the coupling constant, θ and the fields, along with the inclusion of θ-dependent counterterms which vanish upon imposing the equations of motion. These θ-dependent counterterms have no physical effect since they vanish on-shell. This result along with the vanishing of the UV divergent part of the fermionic four-point functions leads to the unexpected conclusion that the one-loop matter sector of the background-field effective action of these theories is one-loop multiplicatively renormalisable on-shell. We also show that the background-field effective action of the gauge sector of the theories considered here receives no θ-dependent UV divergent contributions at one-loop. We thus conclude that these theories are on-shell one-loop multiplicatively renormalisable at first order in θ.

Research paper thumbnail of Monopoles, noncommutative gauge theories in the BPS limit and some simple gauge groups

Journal of High Energy Physics, 2007

For three conspicuous gauge groups, namely, SU(2) , SU(3) and SO(5) , and at first order in the n... more For three conspicuous gauge groups, namely, SU(2) , SU(3) and SO(5) , and at first order in the noncommutative parameter matrix hθ µν , we construct smooth monopole-and, some two-monopole-fields that solve the noncommutative Yang-Mills-Higgs equations in the BPS limit and that are formal power series in hθ µν. We show that there exist noncommutative BPS (multi-)monopole field configurations that are formal power series in hθ µν if, and only if, two a priori free parameters of the Seiberg-Witten map take very specific values. These parameters, that are not associated to field redefinitions nor to gauge transformations, have thus values that give rise to sharp physical effects.

Research paper thumbnail of A note on unimodular N=1, d=4 AdS supergravity

Journal of Cosmology and Astroparticle Physics

Research paper thumbnail of Off-shell unimodular N = 1, d = 4 supergravity

Journal of High Energy Physics

We formulate a unimodular N = 1, d = 4 supergravity theory off shell. We see that the infinitesim... more We formulate a unimodular N = 1, d = 4 supergravity theory off shell. We see that the infinitesimal Grassmann parameters defining the unimodular supergravity transformations are constrained and show that the conmutator of two infinitesinal unimodular supergravity transformations closes on transverse diffeomorphisms, Lorentz transformations and unimodular supergravity transformations. Along the way, we also show that the linearized theory is a supersymmetric theory of gravitons and gravitinos. We see that de Sitter and anti-de Sitter spacetimes are non-supersymmetric vacua of our unimodular supergravity theory.

Research paper thumbnail of Quantum noncommutative ABJM theory: first steps

Journal of High Energy Physics

We introduce ABJM quantum field theory in the noncommutative spacetime by using the component for... more We introduce ABJM quantum field theory in the noncommutative spacetime by using the component formalism and show that it is mathcalN\mathcal{N}mathcalN N = 6 supersymmetric. For the U(1) κ × U(1)−κ case, we compute all one-loop 1PI two and three point functions in the Landau gauge and show that they are UV finite and have well-defined commutative limits θ μν → 0, corresponding exactly to the 1PI functions of the ordinary ABJM field theory. This result also holds for all one-loop functions which are UV finite by power counting. It seems that the noncommutative quantum ABJM field theory is free from the noncommutative IR instabilities.

Research paper thumbnail of Unimodular gravity and the lepton anomalous magnetic moment at one-loop

Journal of Cosmology and Astroparticle Physics

We work out the one-loop contribution to the lepton anomalous magnetic moment coming from Unimodu... more We work out the one-loop contribution to the lepton anomalous magnetic moment coming from Unimodular Gravity. We use Dimensional Regularization and Dimensional Reduction to carry out the computations. In either case, we find that Unimodular Gravity gives rise to the same one-loop correction as that of General Relativity.

Research paper thumbnail of Equivalence of quantum field theories related by theθ-exact Seiberg-Witten map

Physical Review D

The equivalence of the noncommutative U(N) quantum field theories related by the θ-exact Seiberg-... more The equivalence of the noncommutative U(N) quantum field theories related by the θ-exact Seiberg-Witten maps is, in this paper, proven to all orders in the perturbation theory with respect to the coupling constant. We show that this holds for super Yang-Mills theories with N = 0, 1, 2, 4 supersymmetry. A direct check of this equivalence relation is performed by computing the one-loop quantum corrections to the quadratic part of the effective action in the noncommutative U(1) gauge theory with N = 0, 1, 2, 4 supersymmetry.

Research paper thumbnail of Quantum duality under the θ-exact Seiberg-Witten map

Journal of High Energy Physics

We show that in the perturbative regime defined by the coupling constant, the θ-exact Seiberg-Wit... more We show that in the perturbative regime defined by the coupling constant, the θ-exact Seiberg-Witten map applied to the noncommutative U(N) Yang-Mills-with or without Supersymmetry-gives an ordinary gauge theory which is, at the quantum level, dual to the former. We do so by using the on-shell DeWitt effective action and dimensional regularization. We explicitly compute the one-loop two-point function contribution to the on-shell DeWitt effective action of the ordinary U(1) theory furnished by the θ-exact Seiberg-Witten map. We find that the non-local UV divergences found in the propagator in the Feynman gauge all but disappear, so that they are not physically relevant. We also show that the quadratic noncommutative IR divergences are gauge-fixing independent and go away in the Supersymmetric version of the U(1) theory.

Research paper thumbnail of Unimodular trees versus Einstein trees

The European Physical Journal C, 2016

The maximally helicity violating tree-level scattering amplitudes involving three, four or five g... more The maximally helicity violating tree-level scattering amplitudes involving three, four or five gravitons are worked out in Unimodular Gravity. They are found to coincide with the corresponding amplitudes in General Relativity. This a remarkable result, insofar as both the propagators and the vertices are quite different in the two theories.

Research paper thumbnail of U(1){sub A} anomaly in noncommutative SU(N) theories

Phys Rev D, 2005

We work out the one-loop U(1){sub A} anomaly for noncommutative SU(N) gauge theories up to second... more We work out the one-loop U(1){sub A} anomaly for noncommutative SU(N) gauge theories up to second order in the noncommutative parameter θ{sup μ}{sup ν}. We set θ{sup 0i}=0 and conclude that there is no breaking of the classical U(1){sub A} symmetry of the theory coming from the contributions that are either linear or quadratic in θ{sup μ}{sup ν}. Of course, the ordinary anomalous contributions will be still with us. We also show that the one-loop conservation of the nonsinglet currents holds at least up to second order in θ{sup μ}{sup ν}. We adapt our results to noncommutative gauge theories with SO(N) and U(1) gauge groups.

Research paper thumbnail of The light-cone gauge, Chern-Simons theory and topologically massive Yang-Mills theory

In this paper, we complete our study of one-loop perturbative Chern-Simons theoiy in the light-co... more In this paper, we complete our study of one-loop perturbative Chern-Simons theoiy in the light-cone gauge n A" = 0, n 2 = 0. Using a gauge-invariant regularization procedure, which defines Chern-Simons theory as the large-mass limit of a topologically massive field theory, we evaluate the three-point function I',~'(p 1, P2, p3) to one loop. The spurious poles of (q. nY

Research paper thumbnail of Note on the gauge symmetries of unimodular gravity

Physical Review D, 2016

The symmetries of Unimodular Gravity are clarified somewhat.

Research paper thumbnail of Conformal dilaton gravity: Classical noninvariance gives rise to quantum invariance

Physical Review D, 2016

When quantizing Conformal Dilaton Gravity there is a conformal anomaly which starts at two loop o... more When quantizing Conformal Dilaton Gravity there is a conformal anomaly which starts at two loop order. This anomaly stems from evanescent operators on the divergent parts of the effective action. The general form of the finite counterterm which is necessary in order to insure cancellation of the Weyl anomaly to every order in perturbation theory has been determined using only conformal invariance. Those finite counterterms do not have any inverse power of any mass scale in front of them (precisely because of conformal invariance) and then they are not negligible in the low energy deep infrared limit. The general form of the ensuing modifications to the scalar field equation of motion has been determined and some physical consequences extracted.

Research paper thumbnail of Super Yang-Mills and θ-exact Seiberg-Witten map: absence of quadratic noncommutative IR divergences

Journal of High Energy Physics, 2016

We compute the one-loop 1PI contributions to all the propagators of the noncommutative (NC) N = 1... more We compute the one-loop 1PI contributions to all the propagators of the noncommutative (NC) N = 1, 2, 4 super Yang-Mills (SYM) U(1) theories defined by the means of the θ-exact Seiberg-Witten (SW) map in the Wess-Zumino gauge. Then we extract the UV divergent contributions and the noncommutative IR divergences. We show that all the quadratic noncommutative IR divergences add up to zero in each propagator.

Research paper thumbnail of Does Stochastic Analytic Regularization Provide Quantum Field Theories?

Ijmpa, 1992

We analyze whether the so-called method of stochastic analytic regularization is suitable as an i... more We analyze whether the so-called method of stochastic analytic regularization is suitable as an intermediate step for constructing perturbative renormalized quantum field theories. We choose a λϕ3 in six dimensions to prove that this regularization method does not in general provide a quantum field theory. This result seems to apply to any field theory with a quadratically UV-divergent stochastic two-point function, for instance λϕ4 and gauge theories in four dimensions.

Research paper thumbnail of Noncommutative ?? = 1 super Yang-Mills, the Seiberg-Witten map and UV divergences

J High Energy Phys, 2009

Page 1. Noncommutative = 1 super Yang-Mills, the Seiberg-Witten map and UV divergences This artic... more Page 1. Noncommutative = 1 super Yang-Mills, the Seiberg-Witten map and UV divergences This article has been downloaded from IOPscience. ... Noncommutative A = 1 super Yang-Mills, the Seiberg-Witten map and UV divergences CP Mart´ına and C. Tamaritb ...

Research paper thumbnail of Iñaki Gabilondo, ciudadano en Gran Vía: la aventura de 30 años de radio

Research paper thumbnail of Quantum corrections to unimodular gravity

Journal of High Energy Physics, 2015

The problem of the cosmological constant appears in a new light in Unimodular Gravity. In particu... more The problem of the cosmological constant appears in a new light in Unimodular Gravity. In particular, the zero momentum piece of the potential (that is, the constant piece independent of the matter fields) does not automatically produce a cosmological constant proportional to it. The aim of this paper is to give some details on a calculation showing that quantum corrections do not renormalize the classical value of this observable.

Research paper thumbnail of Parameter restrictions in a non-commutative geometry model do not survive standard quantum corrections

Physics Letters B, 1993

We have investigated the standard one-loop quantum corrections for a particularly simple non-comm... more We have investigated the standard one-loop quantum corrections for a particularly simple non-commutative geometry model containing fermions interacting with a unique abelian gauge field and a unique scalar through Yukawa couplings. In this model there are certain relations among the different coupling constants quite similar to the ones appearing in the Connes-Lott version of the standard model. We find that it is not possible to implement those relations in a renormalization-group invariant way.

Research paper thumbnail of Critical exponents at the three-loop level from stochastic continuum regularization

Research paper thumbnail of Renormalisability of noncommutative GUT inspired field theories with anomaly safe groups

Journal of High Energy Physics, 2009

We consider noncommutative GUT inspired field theories formulated within the enveloping-algebra f... more We consider noncommutative GUT inspired field theories formulated within the enveloping-algebra formalism for anomaly safe compact simple gauge groups. Our theories have only gauge fields and fermions, and we compute the UV divergent part of the one-loop background-field effective action involving two fermionic fields at first order in the noncommutativity parameter θ. We show that, if the second-degree Casimir has the same value for all the irreps furnished by the fermionic multiplets of the model, then, that UV divergent part can be renormalised by carrying out multiplicative renormalisations of the coupling constant, θ and the fields, along with the inclusion of θ-dependent counterterms which vanish upon imposing the equations of motion. These θ-dependent counterterms have no physical effect since they vanish on-shell. This result along with the vanishing of the UV divergent part of the fermionic four-point functions leads to the unexpected conclusion that the one-loop matter sector of the background-field effective action of these theories is one-loop multiplicatively renormalisable on-shell. We also show that the background-field effective action of the gauge sector of the theories considered here receives no θ-dependent UV divergent contributions at one-loop. We thus conclude that these theories are on-shell one-loop multiplicatively renormalisable at first order in θ.

Research paper thumbnail of Monopoles, noncommutative gauge theories in the BPS limit and some simple gauge groups

Journal of High Energy Physics, 2007

For three conspicuous gauge groups, namely, SU(2) , SU(3) and SO(5) , and at first order in the n... more For three conspicuous gauge groups, namely, SU(2) , SU(3) and SO(5) , and at first order in the noncommutative parameter matrix hθ µν , we construct smooth monopole-and, some two-monopole-fields that solve the noncommutative Yang-Mills-Higgs equations in the BPS limit and that are formal power series in hθ µν. We show that there exist noncommutative BPS (multi-)monopole field configurations that are formal power series in hθ µν if, and only if, two a priori free parameters of the Seiberg-Witten map take very specific values. These parameters, that are not associated to field redefinitions nor to gauge transformations, have thus values that give rise to sharp physical effects.