Abstract:We continue with the analysis of finite temperature corrections to the Tachyon mass in intersecting branes which was initiated in [1]. In this paper we extend the computation to the case of intersecting D3 branes by considering a setup of two intersecting branes in flat-space background. A holographic model dual to BCS superconductor consisting of intersecting D8 branes in D4 brane background was proposed in [2]. The background considered here is a simplified configuration of this dual model. We compute the one-loop Tachyon amplitude in the Yang-Mills approximation and show that the result is finite. Analyzing the amplitudes further we numerically compute the transition temperature at which the Tachyon becomes massless. The analytic expressions for the one-loop amplitudes obtained here reduce to those for intersecting D1 branes obtained in [1] as well as those for intersecting D2 branes.

A holographic description of BCS superconductivity is given in [1]. This model was constructed by insertion of a pair of D8-branes on a D4-background. The spectrum of intersecting D8-branes has tachyonic modes indicating an instability which is identified with the BCS instability in superconductors. Our aim is to study the stability of the intersecting branes under finite temperature effects. Many of the technical aspects of this problem are captured by a simpler problem of two intersecting D1-branes on flat background. In the simplified set-up we compute the one-loop finite temperature corrections to the treelevel tachyon mass-squared-squared using the frame-work of SU(2) Yang-Mills theory in (1 + 1)-dimensions. We show that the one-loop two-point functions are ultraviolet finite due to cancellation of ultraviolet divergence between the amplitudes containing bosons and fermions in the loop. The amplitudes are found to be infrared divergent due to the presence of massless fields in the loops. We compute the finite temperature mass-squared correction to all the massless fields and use these temperature dependent masses-squared to compute the tachyonic mass-squared correction. We show numerically the existence of a transition temperature at which the effective mass-squared of the tree-level tachyons becomes zero, thereby stabilizing the brane configuration.

Several time dependent backgrounds, with perfect fluid matter, can be used to construct solutions of Einstein equations in the presence of a negative cosmological constant along with some matter sources. In this work we focus on the non-vacuum Kasner-AdS geometry and its solitonic generalization. To characterize these space-times, we provide ways to embed them in higher dimensional flat space-times. General space-like geodesics are then studied and used to compute the two point boundary correlators within the geodesic approximation.

Computation of superstring partition functions for the non-linear sigma model on the product of a two-torus and its dual within the scope of the doubled formalism is presented. We verify that it reproduces the partition functions of the toroidally compactified type-IIA and type-IIB theories for appropriate choices of the GSO projection. * tpspc@mahendra.iacs.res.in corresponding quantum theory is equivalent to the quantum version of the non-linear sigma model defined on a worldsheet of arbitrary genus. A generalization of the formalism to superstring theories has also been worked out [9] . Constraint-quantization of the doubled formalism has been studied too [24,25]. In an attempt to relate results from the new theory with the usual results in string theory, the partition function for the bosonic string on a circle has been calculated in the doubled formalism [26]. In the same vein it is important to compare the results for superstrings and with targets with more than one compact dimensions.Here we consider an N = (1, 1) non-linear sigma model on a doubled torus T 2 × T 2 , where the two-tori T 2 and T 2 are dual to each other in the sense mentioned before. We compute the one-loop partition function of the two-torus. A two-torus is thought of as a direct product of circles, T 2 ≃ S 1 ×S 1 . On each of the circles the superfields are split into ones with left and right chiralities. We write down the constraint equations for superfields on the doubled torus and find that they satisfy the appropriate chirality conditions. These constraints are interpreted as the chiral superfields which is crucial for establishing the quantum consistency of the doubled theory. A supersymmetrically extended topological term is needed for the superconformal invariance of the theory. The bosonic part of the topological term contributes with an overall sign factor to the partition function. The fermionic part of the same, on the other hand, does not contribute. This is of utmost importance for the matching of the partition function with the type-II results.In section 2 we write down the action of the doubled N = (1, 1) NLSM as well as the superfields along with the constraints. The equation of motion for bosons on a torus have instanton solutions. In section 3 we present the computation of the one-loop partition function for the instanton sector for bosons [26] on a twotorus. A Poisson re-summation is required for the holomorphic factorization of the partition function. These computations for the bosons yield the sum over the internal momenta. We discuss the contributions from the bosonic and fermionic oscillators to the partition function, in section 4, in terms of the well-known modular functions. The fermionic contributions to the partition function after suitable GSO projections are found to match with the type-IIA and type-IIB results. Finally in section 5 we draw conclusions from our work.2 The N = (1, 1) NLSM on a doubled torus Let us start with the non-linear sigma model action in N = (1, 1) superspace on a doubled torus, T 2 × ...