arXiv subjects
Publications and source records attributed to Harvendra Singh.
We uplift 5-dimensional super-Yang-Mills theory to a 6-dimensional gauge theory with the help of a space-like constant vector $η^M$, whose norm determines the Yang-Mills coupling constant. After the localization of $η^M$ the 6D gauge theory acquires Lorentzian invariance as well as scale invariance. We discuss KK states, instantons and the flux quantization. The 6D theory admits extended solutions like 1/2 BPS `strings' and monopoles.
We obtain non-relativistic AdS4 X CP3 solutions with dynamical exponent 3 in type IIA string theory, both with and without Romans mass. The compactifications to four dimensions are found to describe Proca fields in anti-de Sitter spacetime. This leads us to conclude that the massive and massless IIA theories should be identified in four dimensions and the Romans mass should be identified with the `flux' along CP3 in a definite manner. From supergravity point of view, it is suggestive of some four-dimensional symmetry that rotates Romans mass into the flux along CP3. We also provide M-theory Galilean ABJM background which gives rise to the nonrelativistic type IIA solution.
Recently we studied `vanishing' horizon limits of `boosted' black D3-brane geometry \cite{hsnr}. The type IIB solutions obtained by taking these special double limits were found to describe nonrelativistic Lifshitz spacetimes at zero temperature. In the present work we study these limits for TsT black-hole solutions which include $B$-field. The new Galilean solutions describe a holographic RG flow from Schrödinger ($a=2$) spacetime in UV to a Lifshitz universe ($a=3$) in the IR.
We study special vanishing horizon limit of `boosted' black D3-branes having a compact light-cone direction. The type IIB solution obtained by taking such a zero temperature limit is found to describe a nonrelativistic system with dynamical exponent 3. We discuss about such limits in M2-branes case also.
The Chern-Simons level k of ABJM gauge theory captures the orbifolding in the dual geometry. This suggests that if we move the membranes away from the tip of the orbifold to a smooth point, it should trigger an RG flow that changes the level to k=1 in the IR. We construct an explicit supergravity solution that is dual to this shift from generic k to k=1. In the gauge theory side, we present arguments for why this shift is plausible at the end of the RG flow. We also consider a resolution of the orbifold for the case k=4 (where explicit metrics can be found), and construct the smooth supergravity solution that interpolates between AdS4 X S7/Z4 and AdS4 X S7, corresponding to localized branes on the blown up six cycle. In the gauge theory, we make some comments about the dimension four operator dual to the resolution as well as the associated RG flow.
The Romans type IIA theory is the only known example of 10-dimensional maximal supergravity where (tensor) fields are explicitly massive. We provide an example of a non-relativistic anti-de Sitter $NRadS_4\times S^6$ background as a solution in massive type IIA. A compactification of which on $S^6$ gives immediately the prototype NRadS background in D=4 which is proposed to be dual to `cold atoms' or unitary fermions on a wire.
This work is based on an earlier proposal \cite{hs} that the membrane B-F theory consists of matter fields alongwith Chern-Simons fields as well as the auxiliary pairs of scalar and tensor fields. We especially discuss the supersymmetry aspects of such a membrane theory. It is concluded that the theory possesses maximal supersymmetry and it is related to the L-BLG theory via a field map. We obtain fuzzy-sphere solution and corresponding tensor field configuration is given.
We write down M2-branes on the resolved $C_4/Z_4$ orbifold space. The resolved spatial geometry is such that it interpolates between $R^2\times CP_3$ near the branes and $C_4/Z_4$ asymptotically. The near horizon geometry of these branes is a deformation of $AdS_4\times S^7/Z_4$. An interesting aspect is that for $k=4$ Chern-Simons theory coupling becomes vanishing near the IR cutoff leading to spontaneous compactification to type IIA.
We construct a SU(N) membrane $B\wedge F$ theory with dual pairs of scalar and tensor fields. The moduli space of the theory is precisely that of $N$ M2-branes on the noncompact flat space. The theory possesses explicit SO(8) invariance and is an extension of the maximal SU(N) super-Yang-Mills theory.
We study the assisted inflation scenario from the rolling of $N$ BPS D3-brane into the NS5-branes, on a transverse geometry of $R^3 \times S^1$, coupled to four dimensional gravity. We assume that the branes are distributed along $S^1$ and the probe D3-branes spin along $R^3$ plane. Qualitatively this process is similar to that of N-tachyon assisted inflation on unstable D-branes. We further study the spinflation scenario numerically and analyze its effect.
We study the effect of rolling of N D3-branes in the vicinity of NS5-branes. We find out that this system coupled with the four dimensional gravity gives the slow roll assisted inflation of the scalar field theory. Once again this expectation is exactly similar to that of N-tachyon assisted inflation on unstable D-branes.
Space-like branes or S-branes are certain class of time dependent solutions of M/string theories having isometries ISO(p+1) $\times$ SO(d-p-2,1), where $d=11,10$ respectively and have singularities at t=0. In \cite{Roy:2006du}, we found that the asymptotically flat S-branes have the structure of generalized Kasner geometry near t=0. In this work we evaluate higher order $α'$ corrections perturbatively to the heterotic string Kasner backgrounds to probe the singularity at t=0. We generally find that the perturbative corrections do not permit us to reach the singular point, as the supergravity framework fails near $t \sim {\sqrt α'}$ blurring the origin of space-like singularities. This is analogous to the concept of stretched horizons in the case of black holes.
We use the approach used by Eguchi-Hanson in constructing four-dimensional instanton metrics and construct a class of regular six-dimensional instantons which are nothing but $S^2\times S^2$ resolved conifolds. We then also obtain D3-brane solutions on these EH-resolved conifolds.
We use the information metric to investigate the moduli space of a U(1) instanton on (anti)self-dual manifolds, finding an $AdS$ geometry similar to that for the moduli space of a Yang-Mills instanton on flat space. We discuss our results from the perspective of gauge/gravity duality.
In continuation of the papers hep-th/0505012 and hep-th/0508101 we investigate the consequences when $N$ open-string tachyons roll down simultaneously. We demonstrate that the $N$-Tachyon system coupled to gravity does indeed give rise to the assisted slow-roll inflation.
It is known that there exist two different classes of time dependent solutions in the form of space-like (or S)-branes in the low energy M/string theory. Accelerating cosmologies are known to arise from S-branes in one class, but not in the other where the time-like holography in the dS/CFT type correspondence may be more transparent. We show how the accelerating cosmologies arise from S-branes in the other class. Although we do not get the de Sitter structure in the lowest order supergravity, the near `horizon' ($t\to 0$) limits of these S-branes are the generalized Kasner metric.
In a recent paper we studied rolling tachyon flat FRW cosmologies, but those admitting only time-reversal asymmetric boundary conditions. The time-reversal symmetric cosmologies have been studied by Sen previously. We show explicitly here that through appropriate choice of initial conditions, the time evolution of the Hubble parameter in these two types of solutions can be made completely identical for $t>0$, except near $t=0$. The rolling tachyon solution also gives rise to necessary inflation. We find that universe does start as a string size object (with string scale $10^{15} GeV$) with a string mass density $\simeq 10^{78} gm. cm^{-3}$ and not with Planck density.
We aim to study rolling tachyon cosmological solutions in de Sitter gravity. The solutions are taken to be flat FRW type and these are not time-reversal symmetric. We find that cosmological constant of our universe has to be fine-tuned at the level of the action itself, as in KKLT string compactification. The rolling tachyon can give rise to required inflation with suitable choice of the initial conditions which include nonvanishing Hubble constant. We also determine an upper bound on the volume of the compactification manifold.