18666187
Topics in Finite Temperature Field Theory
We discuss a few selected topics in finite temperature field theory.
119217104
The thermal chiral anomaly in the Schwinger model
Abstract In the Schwinger model at finite temperature, we derive a closed form result for the chiral anomaly which arises from the long distance behavior of the electric field Das and Frenkel (2011) [1] . We discuss the general properties associated with this thermal anomaly as well as its relation with the “index” of the Dirac operator. We further show that the thermal anomaly, like the zero temperature anomaly which arises from the ultraviolet behavior of the theory, does not receive any contribution from higher loops. Finally, we determine the complete effective action as well as the anomaly functional on both the thermal branches in the closed time path formalism.
118370691
Infrared chiral anomaly at finite temperature
Abstract We study the Schwinger model at finite temperature and show that a temperature dependent chiral anomaly may arise from the long distance behavior of the electric field. At high temperature this anomaly depends linearly on the temperature T and is present not only in the two point function, but also in all even point amplitudes.
15910786
Supersymmetric polytropic gas dynamics
Abstract 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.
46280608
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.
119327271
Duality, monodromy, and integrability of two dimensional string effective action
The monodromy matrix $\mathcal{M}^$ is constructed for the two dimensional tree level string effective action. The pole structure of $\mathcal{M}^$ is derived using its factorizability property. It is found that the monodromy matrix transforms nontrivially under the noncompact 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, $\mathcal{M}^$ for the exactly solvable Nappi-Witten model, both when $B=0$ and $B\ensuremath{\ne}0,$ where these ideas can be directly checked. We consider well known charged black hole solutions in the heterotic string theory that 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.
17456528
Derivative expansion and large gauge invariance at finite temperature
We study the 0+1 dimensional Chern-Simons theory at finite temperature within the framework of derivative expansion. We obtain various interesting relations, solve the theory within this framework and argue that the derivative expansion is not a suitable formalism for a study of the question of large gauge invariance.
121691299
Strong-coupling approximation in supersymmetric field theory
Abstract We show how to use the lattice strong-coupling approximation in a wide class of two-dimensional supersymmetric field theories. We demonstrate that this technique is highly accurate for supersymmetric theories by calculating the ground-state energy density E 0 through seventh order in perturbation theory and by showing that the result approaches the correct supersymmetric limit E 0 =0. We argue that, by their nature, strong-coupling methods are especially well-suited for practical calculation in supersymmetric theories.
17584637
ON THE WARD IDENTITIES AT FINITE TEMPERATURE
We show in both 1+1 and 3+1 dimensions that, contrary to the recent suggestions, the contribution of the fermion loop to the polarization tensor is manifestly transverse at finite temperature. Some subtleties associated with the Ward identities at finite temperature are also pointed out.
121579857
The zero curvature formulation of the Boussinesq equation
Abstract We derive the Boussineq equation from the zero curvature condition associated with the group SL (3, R ). We also present a connection between this formulation and the one based on a combined conformal and spin-3 flow.
119899153
Integrable Models and Spin Algebras
We show how the entire KdV hierarchy as well as the recursion relation between the conserved quantities can be obtained from a spin-2 flow. The relationship between this approach and the zero curvature formulation of the KdV system based on the group SL(2, R) is clarified. We show that the Boussinesq equation can be derived as a flow of the spin-3 transformations. The Boussinesq hierarchy, as well as the relevant Lenard relation, is derived from a combined flow of the spin-2 and spin-3 transformations. We have also given an independent derivation of the Lenard relation for the Boussinesq equation starting from the third order Schrodinger equation.