17283472
Large gauge Ward identity
Abstract We study the question of the Ward identity for ` large' gauge invariance in 0+1 dimensional theories. We derive the relevant Ward identities for a single flavor fermion and a single flavor complex scalar field interacting with an Abelian gauge field. These identities are nonlinear. The Ward identity for any other complicated theory can be derived from these basic sets of identities. However, the structure of the Ward identity changes since these are nonlinear identities. In particular, we work out the ` large' gauge Ward identity for a supersymmetric theory involving a single flavor of fermion as well as a complex scalar field. Contrary to the effective action for the individual theories, the solution of the Ward identity in the supersymmetric theory involves an infinity of Fourier component modes. We comment on which features of this analysis are likely/unlikely to generalize to the 2+1 dimensional theory.
18666187
Topics in Finite Temperature Field Theory
We discuss a few selected topics in finite temperature field theory.
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.
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.
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.
1401133
The Supersymmetric two boson hierarchy
We summarize all the known properties of the supersymmetric integrable Two Boson equation. We present its nonstandard Lax formulation and tri-Hamiltonian structure, its reduction to the supersymmetric nonlinear Schrödinger equation and the local as well as nonlocal conserved charges. We also present the algebra of the conserved charges and identify its second Hamiltonian structure with the twisted N = 2 superconformal algebra.
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.
14562531
On neutrino masses and mixings from extra dimensions
Abstract In the framework of a Kaluza-Klein type theory with the Standard Model fields localized on a 4-dimensional section while gravity propagates in a full 4+ δ -dimensional space-time, we examine a mechanism of naturally small neutrino mass generation through couplings of the Standard Model singlet fermion(s) living also in the full space-time. A numerical study is carried out on the charged current universality constraint from the ratio of pion decay partial widths. The bounds obtained on the fundamental mass scale could be stringent.
16189512
Exact effective action for (1+1)-dimensional fermions in an Abelian background at finite temperature
In an effort to further understand the structure of effective actions for fermions in an external gauge background at finite temperature, we study the example of (1+1)-dimensional fermions interacting with an arbitrary Abelian gauge field. We evaluate the effective action exactly at finite temperature. This effective action is non-analytic as is expected at finite temperature. However, contrary to the structure at zero temperature and contrary to naive expectations, the effective action at finite temperature has interactions to all (even) orders (which, however, do not lead to any quantum corrections). The covariant structure thus obtained may prove useful in studying (2+1)-dimensional models in arbitrary backgrounds. We also comment briefly on the solubility of various (1+1)-dimensional models at finite temperature. {copyright} {ital 1999} {ital The American Physical Society}
117190207
Introduction to Gauge Theories and Unification
The theories which we will study in these lectures are supposed to describe fundamental processes at extremely high energies. Consequently, these theories will be relativistic theories invariant under Lorentz transformations. Let me, therefore, begin by establishing some notation which I will be using throughout the lectures.