Shibaji Roy

Accelerating cosmologies from M/String theory compactifications

Abstract We point out that the solution of (4+n)-dimensional gravity coupled to the dilaton and an n-form field strength can give rise to a flat 4-dimensional universe (with a scale factor) of the type proposed recently under time dependent compactifications. The compact internal spaces could be hyperbolic, flat or spherical and the solution is identical to the space-like two brane or S2-brane. As has been shown previously for SM2 solution with a fixed field strength we show that for n=7 (where the dilaton is vanishing and with a general field strength), 6 the corresponding SM2 and SD2 solutions can give accelerating cosmologies in Einstein frame for both hyperbolic and flat internal spaces, thereby meeting the challenge of obtaining such a solution from M/String theory compactifications.

Lifshitz-like space-time from intersecting branes in string/M theory

A bstractWe construct 1/4 BPS, threshold F-Dp bound states (with 0 ≤ p ≤ 5) of type II string theories by applying S- and T-dualities to the D1-D5 system of type IIB string theory. These are different from the known 1/2 BPS, non-threshold F-Dp bound states. The near horizon limits of these solutions yield Lifshitz-like space-times with varying dynamical critical exponent z = 2(5 − p)/(4 − p), for p = 4, along with the hyperscaling violation exponent θ = p − (p − 2)/(4 − p), showing how Lifshitz-like space-time can be obtained from string theory. The dilatons are in general non-constant (except for p = 1). We discuss the holographic RG flows and the phase structures of these solutions. For p = 4, we do not get a Lifshitz-like space-time, but the near horizon limit in this case leads to an AdS2 space.

Non-threshold (F, Dp) bound states

In the previous paper [hep-th/9904112], we argued that there exist BPS bound states of Dp branes carrying certain units of quantized constant electric field for every p (with 1 ⩽ p ⩽ 8). Each of these bound states preserves one half of the spacetime supersymmetries. In this paper, we construct these bound state configurations explicitly for 2 ⩽ p ⩽ 7 from Schwarzs (m, n)-string or (F, D1) bound state in type IIB string theory by T-dualities along the transverse directions. We calculate the charge per (2π)p−1α′(p−1)2 of (p − 1)-dimensional area for F-strings in (F,Dp) and the tension for each of these bound states. The results agree precisely with those obtained previously from the worldvolume study. We study the decoupling limit for the (F, D3) bound state and find that Maldacenas AdS5/CFT4 correspondence may hold true even with respect to this bound state but now with an effective string coupling rather than the usual string coupling. This coupling is quantized and can be independent of the usual string coupling in a certain limit.

((F, D1), D3) bound state, S-duality and noncommutative open string/Yang-Mills theory

We study decoupling limits and S-dualities for non-commutative open string/Yang-Mills theory in a gravity setup by considering an SL(2;Z) invariant supergravity solutions of the form ((F, D1), D3) bound state of type-IIB string theory. This conguration can be regarded as D3-brane solution with both electric and magnetic elds turned on along one of the spatial directions of the brane and preserves half of the space-time supersymmetries of the string theory. Our study indicates that there exists a decoupling limit for which the resulting theory is an openstring theorydened inageometry withnoncommutativity inbothspace-time andspace-space directions. WestudyS-dualityofthisnon-commutative openstring (NCOS) and nd that the same decoupling limit in the S-dual description gives rise to a space-space non-commutative Yang-Mills theory (NCYM). We also discuss independentlythedecouplinglimitforNCYMinthisD3-branebackground. Herewe nd that S-duality of NCYM theory does not always give a NCOS theory. Instead, it cangiveanordinaryYang-Millswithsingularmetricandinnitelylargecoupling. WealsondthattheopenstringcouplingrelationbetweenthetwoS-dualityrelated theoriesismodiedsuchthatS-dualityofastronglycoupledopen-string/Yang-Mills theory does not necessarily give a weakly coupled theory. The relevant gravity dual descriptions of NCOS/NCYM are also given.

Static, non-SUSY p-branes in diverse dimensions

We give explicit constructions of static, non-supersymmetric p-brane (for p• di 4, where d is the space-time dimensionality and including p = i1 or D-instanton) solutions of type II supergravities in diverse dimensions. A subclass of these are the static counterpart of the time dependent solutions obtained in (3). Depending on the forms of the non-extremality function G(r) deflned in the text, we discuss various possible solutions and their region of validity. We show how one class of these solutions interpolate between the p-brane{anti-p-brane solutions and the usual BPS p-brane solutions in d = 10, while the other class, although have BPS limits, do not have such an interpretation. We point out how the time dependent solutions mentioned above can be obtained by a Wick rotation of one class of these static solutions. We also discuss another type of solutions which might seem non-supersymmetric, but we show by a coordinate transformation that they are nothing but the near horizon limits of the various BPS p-branes already known.

((F, D1), D3) bound state and its T-dual daughters

In the previous paper [hep-th/9904129], we constructed a general explicit BPS solution for (F,D3) non-threshold bound state. By using the SL(2,) symmetry of type-IIB string theory, we here construct from (F,D3) a more general BPS configuration for a D3 brane with certain units of quantized 5-form flux and an infinite number of parallel (F,D1)-strings. We study its decoupling limit and find that given Maldacenas AdS5/CFT4 correspondence with respect to simple D3-branes and with the usual string coupling, we should have a similar correspondence with respect to this bound state but now with an effective string coupling. We discuss possible descendants of this bound state by T-dualities along its longitudinal or transverse directions. In particular, we present explicit configurations for ((F, Dp),D(p+2)) bound states for 2 ≤ p ≤ 5. All these configurations preserve one half of the spacetime supersymmetries.

Lifshitz metric with hyperscaling violation from NS5-Dp states in string theory

Abstract In previous papers Dey and Roy (2012) [1] , [2] we have shown how Lifshitz-like space–time (space–time having a Lifshitz scaling along with a hyperscaling violation) can arise by taking near horizon limits of certain intersecting solutions (F-string with Dp-branes and also with two D-branes) of string theory. In this Letter we construct intersecting bound state solutions in the form of NS5-Dp-branes (with 1 ⩽ p ⩽ 6 ) of type II string theories. These are 1/4 BPS and threshold bound states unlike the known NS5-Dp bound states which are 1/2 BPS and non-threshold. We show that the near horizon limits of these solutions also lead to Lifshitz-like space–time with the dynamical scaling exponent z = 0 and the hyperscaling violation exponent θ = 9 − p . The spatial dimension of the boundary theory is d = 7 − p . The dilatons in these theories are not constant in general (except for p = 5 ) and therefore produce RG flows. So, we also consider the strong coupling phases of these theories and find that these phases also have similar Lifshitz-like structures, except for p = 2 , where it has an AdS3 structure.

SL(2,Z) duality and 4-dimensional noncommutative theories

We investigate how the four-dimensional noncommutative open string/Yang-Mills theory behaves under a general non-perturbative quantum

(NS5,Dp) and (NS5,D(p+2),Dp) bound states of type IIB and type IIA string theories

SL(2,Z)

(p+1) -Dimensional noncommutative Yang–Mills and D(p−2) branes

symmetry transformation. We discuss this by considering D3 branes in a constant background of axion, dilaton, and electric and magnetic fields (including both