119009436
Duality and integrability of two-dimensional string effective action
Abstract We present a prescription for constructing the monodromy matrix, 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 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 ≠0.
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.
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.
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.
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.
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.
18810830
The sTB-B hierarchy
Abstract We construct a new supersymmetric two boson (sTB-B) hierarchy and study its properties. We derive the conserved quantities and the Hamiltonian structures (proving the Jacobi identity) for the system. We show how this system gives the sKdV-B equation and its Hamiltonian structures upon appropriate reduction. We also describe the zero curvature formulation of this hierarchy both in the superspace as well as in components.
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.
121901630
Super-Higgs effect in a new class of scalar models and a model of super QED
We present results on the scalar supermultiplet coupled to supergravity. A locally supersymmetric theory with generalized kinetic and nonderivative interaction terms is found. We discuss a number of examples. Symmetry breakdown and the "super-Higgs" effect are studied, as is a consistent truncation of the SO(4) extended theory. Finally, we find the local extension of supersymmetric massless QED and discuss symmetry breakdown in this system.
123687308
Supersymmetry at high temperatures
We investigate the properties of Green's functions in a spontaneously broken supersymmetric model at high temperatures. We show that, even at high temperatures, we do not get restoration of supersymmetry, at least in the one-loop approximation.
15974936
A NOTE ON ABELIAN CONVERSION OF CONSTRAINTS
We show that for a system containing a set of general second class constraints which are linear in the phase space variables, the Abelian conversion can be obtained in a closed form and that the first class constraints generate a generalized shift symmetry. We study in detail the example of a general first order Lagrangian and show how the shift symmetry noted in the context of BV quantization arises.