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Ashok Das

Publications and source records attributed to Ashok Das.

At least 91 records · Page 5Linked to original sources
arXiv2002

Transport equation and hard thermal loops in noncommutative Yang-Mills theory

We show that the high temperature limit of the noncommutative thermal Yang-Mills theory can be directly obtained from the Boltzmann transport equation of classical particles. As an illustration of the simplicity of the Boltzmann method, we evaluate the two and the three-point gluon functions in the noncommutative U(N) theory at high temperatures T. These amplitudes are gauge invariant and satisfy simple Ward identities. Using the constraint satisfied at order T^2 by the covariantly conserved current, we construct the hard thermal loop effective action of the noncommutative theory.

hep-th↗
arXiv2002

Generalized Benney Lattice and the Heavenly Equation

We generalize the Benney lattice and show that the new system of equations can be reduced to a generalized Chaplygin gas as well as the heavenly equation. We construct two infinite sets of conserved charges and show that one of the sets can be obtained from the Lax function. The conserved densities are related to Legendre polynomials and we present closed form expressions for the generating functions for these densities which also determines the Riemann invariants of the problem. We prove that the system is bi-Hamiltonian and that the conserved charges are in involution with respect to either of the Hamiltonian structures. We show that the associated generalized elastic medium equations are bi-Hamiltonian as well. We also bring out various other interesting features of our model.

nlin.SI↗
arXiv2002

A systematic study of the radion in the compact Randall-Sundrum model

We systematically study the question of identification and consistent inclusion of the radion, within the Lagrangian approach, in a two brane Randall-Sundrum model. Exploiting the symmetry properties of the theory, we show how the radion can be identified unambiguously and give the action to all orders in the radion field and the metric. Using the background field method, we expand the theory to quadratic orders in the fields. We show that the most general classical solutions, for the induced metric on the branes in the case of a constant radion and a factorizable 4D metric, correspond to Einstein spaces. We discuss extensively the diagonalization of the quadratic action. Furthermore, we obtain the 4-dimensional effective theory from this and study the question of the spectrum as well as the couplings in these theories.

hep-th↗
arXiv2002

Screening Length in 2+1-dimensional Abelian Chern-Simons Theories

In this paper, we systematically study the question of screening length in Abelian Chern-Simons theories. In the Abelian Higgs theory, where there are two massive poles in the gauge propagator at the tree level, we show that the coefficient of one of them becomes negligible at high temperature and that the screening length is dominantly determined by the parity violating part of the self-energy. In this theory, static magnetic fields are screened. In the fermion theory, on the other hand, the parity conserving part of the self-energy determines the screening length and static magnetic fields are not screened. Several other interesting features are also discussed.

hep-th↗
arXiv2002

Duality and Integrability of Two Dimensional String Effective Action

We present a prescription for constructing the monodromy matrix, $\hat{\cal M}(ω)$, for $O(d,d)$ invariant string effective actions and derive its transformation properties under the $T$-duality group. This allows us to construct $\hat{\cal M}(ω)$ for new backgrounds, starting from known ones, which are related by $T$-duality. As an application, we derive the monodromy matrix for the exactly solvable Nappi-Witten model, both when B=0 and $B\neq 0$.

hep-th↗
arXiv2002

Duality, Monodromy and Integrability of Two Dimensional String Effective Action

The monodromy matrix, ${\hat{\cal M}}$, is constructed for two dimensional tree level string effective action. The pole structure of ${\hat{\cal M}}$ is derived using its factorizability property. It is found that the monodromy matrix transforms non-trivially under the non-compact T-duality group, which leaves the effective action invariant and this can be used to construct the monodromy matrix for more complicated backgrounds starting from simpler ones. We construct, explicitly, ${\hat{\cal M}}$ for the exactly solvable Nappi-Witten model, both when B=0 and $B\neq 0$, where these ideas can be directly checked. We consider well known charged black hole solutions in the heterotic string theory which can be generated by T-duality transformations from a spherically symmetric `seed' Schwarzschild solution. We construct the monodromy matrix for the Schwarzschild black hole background of the heterotic string theory.

hep-th↗
arXiv2002

General structure of the photon self-energy in non-commutative QED

We study the behavior of the photon two point function, in non-commutative QED, in a general covariant gauge and in arbitrary space-time dimensions. We show, to all orders, that the photon self-energy is transverse. Using an appropriate extension of the dimensional regularization method, we evaluate the one-loop corrections, which show that the theory is renormalizable. We also prove, to all orders, that the poles of the photon propagator are gauge independent and briefly discuss some other related aspects.

hep-th↗
arXiv2001

Non-Abelian Thermal Large Gauge Transformations in 2+1 Dimensions

We discuss several different constructions of non-Abelian large gauge transformations at finite temperature. Pisarski's ansatz with even winding number is related to Hopf mappings, and we present a simple new ansatz that has any integer winding number at finite temperature.

hep-th↗
arXiv2001

Induced parity violating thermal effective action for (2+1)-dimensional fermions interacting with a non-Abelian background

We study the parity breaking effective action in 2+1 dimensions, generated, at finite temperature, by massive fermions interacting with a non-Abelian gauge background. We explicitly calculate, in the static limit, parity violating amplitudes up to the seven point function, which allows us to determine the corresponding effective actions. We derive the exact parity violating effective action when $\vec{E}=0$. When $\vec{E}\neq 0$, there are families of terms that can be determined order by order in perturbation theory. We attempt to generalize our results to non-static backgrounds through the use of time ordered exponentials and prove gauge invariance, both {\it small} and {\it large}, of the resulting effective action. We also point out some open questions that need to be further understood.

hep-th↗
arXiv2001

Parity Violating Bosonic Loops at Finite Temperature

The finite temperature parity-violating contributions to the polarization tensor are computed at one loop in a system without fermions. The system studied is a Maxwell-Chern-Simons-Higgs system in the broken phase, for which the parity-violating terms are well known at zero temperature. At nonzero temperature the static and long-wavelength limits of the parity violating terms have very different structure, and involve non-analytic log terms depending on the various mass scales. At high temperature the boson loop contribution to the Chern-Simons term goes like T in the static limit and like T log T in the long-wavelength limit, in contrast to the fermion loop contribution which behaves like 1/T in the static limit and like log T/T in the long wavelength limit.

hep-th↗
arXiv2001

Selected topics in integrable models

In these talks, I discuss a few selected topics in integrable models that are of interest from various points of view. Some open questions are also described.

hep-th↗
arXiv2001

Noncommutativity of Boundary Closed String Coordinates for an Open Membrane on p-Brane

We study the dynamics of an open membrane with a cylindrical topology, in the background of a constant three form. We use the action, due to Bergshoeff, London and Townsend, to study the noncommutativity properties of the boundary string coordinates. The constrained Hamiltonian formalism due to Dirac is used to derive the noncommutativity of coordinates. The chain of constraints is found to be finite for a suitable gauge choice.

hep-th↗
arXiv2001

Lucas polynomials and a standard Lax representation for the polytropic gas dynamics

A standard Lax representation for the polytropic gas dynamics is derived by exploiting various properties of the Lucas and Fibonacci polynomials. The two infinite sets of conserved charges are derived from this representation and shown to coincide with the ones derived from the known non-standard representation. The same Lax function is shown to also give the standard Lax description for the elastic medium equations. In addition, some results on possible dispersive extensions of such models are presented.

hep-th↗
arXiv2001

Supersymmetric Polytropic Gas Dynamics

We construct the N=1 supersymmetric extension of the polytropic gas dynamics. We give both the Lagrangian as well as the Hamiltonian description of this system. We construct the infinite set of "Eulerian'' conserved charges associated with this system and show that they are in involution, thereby proving complete integrability of this system. We construct the SUSY -B extension of this system as well and comment on the similarities and differences between this system and an earlier construction of the supersymmetric Chaplygin gas. We also derive the N=1 supersymmetric extension of the elastic medium equations, which, however, do not appear to be integrable.

hep-th↗
arXiv2001

Colliding String Waves and Duality

The collision of plane waves corresponding to massless states of closed string is considered in $D$-dimensional space-time. The reduced tree level effective action is known to be manifestly $O(d,d)$ invariant, $d$ being the number of transverse spatial dimensions in the collision process. We adopt a coset space reformulation of the effective two dimensional theory and discuss the relation of this process with classical integrable systems in two dimensions in the presence of gravity. We show how it is possible to generate new backgrounds for the scattering process, from known background solutions to the equations of motion, in the coset reformulation. We present explicit calculations for the case of four space-time dimensions as an illustrative example.

hep-th↗
arXiv2001

Properties of Moyal-Lax Representation

The Moyal-Lax representation and the Moyal momentum algebra are introduced and systematically investigated. It is shown that the Moyal-Lax equation can be interpreted as a Hamiltonian equation and can be derived from an action. We show that the parameter of non-commutativity, in this case, is related to the central charge of the second Hamiltonian structure of the system. The Moyal-Lax description leads in a natural manner to the dispersionless limit and provides the second Hamiltonian structure of dispersionless integrable models, which has been an open question for sometime.

hep-th↗