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.
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.
119493925
Kontsevich product and gauge invariance
We analyze the question of ${U}_{\ensuremath{\star}}(1)$ gauge invariance in a flat noncommutative space where the parameter of noncommutativity, ${\ensuremath{\theta}}^{\ensuremath{\mu}\ensuremath{\nu}}(x),$ is a local function satisfying the Jacobi identity (and thereby leading to an associative Kontsevich product). We show that in this case both gauge transformations as well as the definitions of covariant derivatives have to be modified so as to have a gauge invariant action. We work out the gauge invariant actions for the matter fields in the fundamental and the adjoint representations up to order ${\ensuremath{\theta}}^{2}$ while we discuss the gauge invariant Maxwell theory up to order $\ensuremath{\theta}.$ We show that, despite the modifications in the gauge transformations, the covariant derivative, and the field strength, the Seiberg-Witten map continues to hold for this theory. In this theory, translations do not form a subgroup of the gauge transformations (unlike in the case when ${\ensuremath{\theta}}^{\ensuremath{\mu}\ensuremath{\nu}}$ is a constant) which is reflected in the stress tensor not being conserved.
119290439
An alternative construction of the positive inner product in non-Hermitian quantum mechanics
Within the context of non-Hermitian quantum mechanics, we use the generators of eigenvectors of the Hamiltonian to construct a unitary inner product space. Such models have been of interest in recent years, for instance, in the context of PT symmetry, although our construction extends to the larger class of so-called pseudo-Hermitian operators. We provide a detailed example to illustrate the concept and compare with known results.
119183441
The structure of supersymmetry in PT symmetric quantum mechanics
The structure of supersymmetry is analyzed systematically in PT symmetric quantum mechanical theories. We give a detailed description of supersymmetric systems associated with one-dimensional PT symmetric quantum mechanical theories. We show that there is a richer structure present in these theories compared to the conventional theories associated with Hermitian Hamiltonians. We bring out various properties associated with these supersymmetric systems and generalize such quantum mechanical theories to higher dimensions as well as to the case of one-dimensional shape invariant potentials.
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.
119187662
DARBOUX TRANSFORMATION AND MULTI-SOLITON SOLUTIONS OF TWO-BOSON HIERARCHY
We study Darboux transformations for the two boson (TB) hierarchy both in the scalar as well as in the matrix descriptions of the linear equation. While Darboux transformations have been extensively studied for integrable models based on SL(2, R) within the AKNS framework, this model is based on SL(2, R)⊗U(1). The connection between the scalar and the matrix descriptions in this case implies that the generic Darboux matrix for the TB hierarchy has a different structure from that in the models based on SL(2, R) studied thus far. The conventional Darboux transformation is shown to be quite restricted in this model. We construct a modified Darboux transformation which has a much richer structure and which also allows for multi-soliton solutions to be written in terms of Wronskians. Using the modified Darboux transformations, we explicitly construct one-soliton/kink solutions for the model.
15048456
INTEGRABLE MODELS AND THE HIGHER DIMENSIONAL REPRESENTATIONS OF GRADED LIE ALGEBRAS
We construct a zero curvature formulation, in superspace, for the sTB-B hierarchy which naturally reduces to the zero curvature condition in terms of components, thus solving one of the puzzling features of this model. This analysis, further, suggests a systematic method of constructing higher dimensional representations for the zero curvature condition starting with the fundamental representation. We illustrate this with the examples of the sTB hierarchy and the sKdV hierarchy. This would be particularly useful in constructing explicit higher dimensional representations of graded Lie algebras.
45783134
Thermal operator representation of feynman graphs
In this talk I describe an interesting relation between Feynman graphs at finite temperature and chemical potential and the corresponding ones at zero temperature. The operator relating the two which we call the "thermal operator", simplifies the evaluation of finite temperature graphs and helps in understanding better several physical questions such as cutting rules, forward scattering, gauge invariance etc at finite temperature.
17713966
Proper Time Method for Fermions
We show how Schwinger's proper time method can be used to evaluate directly the determinant of first order operators associated with fermionic theories. Several examples are worked out in detail.
9495818
ON M-THEORY AND THE SYMMETRIES OF TYPE II STRING EFFECTIVE ACTIONS
We study the “ordinary” Scherk-Schwarz dimensional reduction of the bosonic sector of the low energy effective action of a hypothetical M-theory on S1 × S1 ≊ T2. We thus obtain the low energy effective actions of type IIA string theory in both ten and nine space-time dimensions. We point out how to obtain the O(1,1) invariance of the NS-NS sector of the string effective action correctly in nine dimensions. We dimensionally reduce the type IIB string effective action on S1 and show that the resulting nine-dimensional theory can be mapped, purely from the bosonic consideration, exactly to the type IIA theory by an O(1,1) or Buscher's T-duality transformations. We then give a dynamical argument, in analogy with that for the type IIB theory in ten dimensions, to show how an S-duality in the type IIA theory can be understood from the underlying nine-dimensional theory by compactifying M-theory on a T-dual torus T2.