124322319
A simple and direct method for generating travelling wave solutions for nonlinear integrable equations
120503298
Systematic expansion for compact QED near weak coupling
123610301
The hamiltonian structures of the KP hierarchy
Abstract We obtain the two hamiltonian structures of the KP hierarchy following the method of Drinfeld and Sokolov. We point out how the second structure of Drinfeld and Sokolov needs to be modified in the present case. We briefly comment on the connection between these structures and the W 1+∞ algebra.
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.
121912240
Chiral Schwinger model in curved space-time
We extend the method of path integrals to obtain the solution of the chiral Schwinger model in curved space-time and compare it with the flat space-time solution.
28025238
Dirac quantization in superspace.
We extend the method of Dirac quantization to superspace. We study simple models like the supersymmetric quantum mechanics as well as the supersymmetric nonlinear \ensuremath{\sigma} model in 1+1 dimensions. Although in both these cases the matrix representing the Poisson brackets between the constraints is singular, we show, following the spirit of Dirac, that one can still define Dirac brackets and that the resulting quantization is consistent with those of the component fields.
119181006
Thermal effective action for 1+1 dimensional massive QED
In continuation of our earlier proposal [A. Das and J. Frenkel, Phys. Lett. B 680, 195 (2009).] and [A. Das and J. Frenkel, Phys. Rev. D 80, 125039 (2009).] for evaluating thermal effective actions, we determine the exact fermion propagator in 1+1 dimensional massive QED. This propagator is used to derive the finite temperature effective action of the theory which generates systematically all the one loop Feynman amplitudes calculated in thermal perturbation theory. Various aspects of the effective action, including its imaginary part are discussed.
119054229
Colliding string waves and duality
Abstract 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.
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.
17654487
OPEN MEMBRANES, p-BRANES AND NONCOMMUTATIVITY OF BOUNDARY STRING COORDINATES
We study the dynamics of an open membrane with a cylindrical topology, in the background of a constant three form, whose boundary is attached to p-branes. The boundary closed string is coupled to a two form potential to ensure gauge invariance. 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, unlike the case of the static gauge, where the chain has an infinite sequence of terms. It is conjectured that the formulation of closed string field theory may necessitate introduction of a star product which is both non commutative and non associative.
15081073
Supersymmetric Moyal-Lax representation
The super Moyal–Lax representation and the super Moyal momentum algebra are introduced and the properties of simple and extended supersymmetric integrable models are systematically investigated. It is shown that, much like in the bosonic cases, the super Moyal–Lax equation can be interpreted as a Hamiltonian equation and can be derived from an action. Similarly, 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 super Moyal– Lax description allows us to go to the dispersionless limit of these models in a singular limit and we discuss some of the properties of such systems.