arXiv subjects

Sumit R. Das

Publications and source records attributed to Sumit R. Das.

At least 55 records · Page 3Linked to original sources

arXiv2011

Quantum Quench across a Holographic Critical Point

We study the problem of quantum quench across a critical point in a strongly coupled field theory using AdS/CFT techniques. The model involves a probe neutral scalar field with mass-squared $m^2$ in the range $-9/4 < m^2 < -3/2$ in a $AdS_4$ charged black brane background. For a given brane background there is a critical mass-squared, $m_c^2$ such that for $m^2 < m_c^2$ the scalar field condenses. The theory is critical when $m^2 = m_c^2$ and the source for the dual operator vanishes. At the critical point, the radial operator for the bulk linearized problem has a zero mode. We study the dynamics of the order parameter with a time dependent source $J(t)$, or a null-time dependent bulk mass $m(u)$ across the critical point. We show that in the critical region the dynamics for an initially slow variation is dominated by the zero mode : this leads to an effective description in terms of a Landau-Ginsburg type dynamics with a {\em linear} time derivative. Starting with an adiabatic initial condition in the ordered phase, we find that the order parameter drops to zero at a time $t_\star$ which is later than the time when $(m_c^2-m^2)$ or $J$ hits zero. In the critical region, $t_\star$, and the departure of the order parameter from its adiabatic value, scale with the rate of change, with exponents determined by static critical behavior. Numerical results for the order parameter are consistent with these expectations.

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arXiv2011

On Dumb Holes and their Gravity Duals

Inhomogeneous fluid flows which become supersonic are known to produce acoustic analogs of ergoregions and horizons. This leads to Hawking-like radiation of phonons with a temperature essentially given by the gradient of the velocity at the horizon. We find such acoustic dumb holes in charged conformal fluids and use the fluid-gravity correspondence to construct dual gravity solutions. A class of quasinormal modes around these gravitational backgrounds perceive a horizon. Upon quantization, this implies a thermal spectrum for these modes.

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arXiv2010

Probe Branes, Time-dependent Couplings and Thermalization in AdS/CFT

We present holographic descriptions of thermalization in conformal field theories using probe D-branes in AdS X S space-times. We find that the induced metrics on Dp-brane worldvolumes which are rotating in an internal sphere direction have horizons with characteristic Hawking temperatures even if there is no black hole in the bulk AdS. The AdS/CFT correspondence applied to such systems indeed reveals thermal properties such as Brownian motions and AC conductivities in the dual conformal field theories. We also use this framework to holographically analyze time-dependent systems undergoing a quantum quench, where parameters in quantum field theories, such as a mass or a coupling constant, are suddenly changed. We confirm that this leads to thermal behavior by demonstrating the formation of apparent horizons in the induced metric after a certain time.

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arXiv2010

Compact $z=2$ Electrodynamics in 2+1 dimensions: Confinement with gapless modes

We consider 2+1 dimensional compact U(1) gauge theory at the Lifshitz point with dynamical critical exponent $z=2$. As in the usual $z=1$ theory, monopoles proliferate the vacuum for any value of the coupling, generating a mass scale. The theory of the dilute monopole gas is written in terms a non-relativistic Sine-Gordon model with two real fields. While monopoles remove some of the massless poles of the perturbative field strength propagator, a gapless mode representing the incomplete screening of monopoles remains, and is protected by a shift invariance of the original theory. Timelike Wilson loops still obey area laws, implying that minimal charges are confined, but the action of spacelike Wilson loops of linear size L goes instead as $L^3$.

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arXiv2009

Slowly Varying Dilaton Cosmologies and their Field Theory Duals

We consider a deformation of the $AdS_5\times S^5$ solution of IIB supergravity obtained by taking the boundary value of the dilaton to be time dependent. The time dependence is taken to be slowly varying on the AdS scale thereby introducing a small parameter $ε$. The boundary dilaton has a profile which asymptotes to a constant in the far past and future and attains a minimum value at intermediate times. We construct the sugra solution to first non-trivial order in $ε$, and find that it is smooth, horizon free, and asymptotically $AdS_5\times S^5$ in the far future. When the intermediate values of the dilaton becomes small enough the curvature becomes of order the string scale and the sugra approximation breaks down. The resulting dynamics is analysed in the dual SU(N) gauge theory on $S^3$ with a time dependent coupling constant which varies slowly. When $N ε\ll 1$, we find that a quantum adiabatic approximation is applicable, and use it to argue that at late times the geometry becomes smooth $AdS_5\times S^5$ again. When $N ε\gg 1$, we formulate a classical adiabatic perturbation theory based on coherent states which arises in the large $N$ limit. For large values of the 'tHooft coupling this reproduces the supergravity results. For small 'tHooft coupling the coherent state calculations become involved and we cannot reach a definite conclusion. We argue that the final state should have a dual description which is mostly smooth $AdS_5$ space with the possible presence of a small black hole.

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arXiv2009

$CP^{N-1}$ Models at a Lifshitz Point

We consider $CP^{N-1}$ models in $d+1$ dimensions around Lifshitz fixed points with dynamical critical exponent $z$, in the large-N expansion. It is shown that these models are asymptotically free and dynamically generate a mass for the $CP^{N-1}$ fields for all $d=z$. We demonstrate that, for $z=d=2$, the initially nondynamical gauge field acquires kinetic terms in a way similar to usual $CP^{N-1}$ models in 1+1 dimensions. Lorentz invariance emerges generically in the low-energy electrodynamics, with a nontrivial dielectric constant given by the inverse mass gap and a magnetic permeability which has a logarithmic dependence on scale. At a special multicritical point, the low-energy electrodynamics also has $z=2$, and an essentially singular dependence of the effective action on $B=ε_{ij}\partial_iA_j$.

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arXiv2009

Gauge Theories with Time Dependent Couplings and their Cosmological Duals

We consider the N=4 SYM theory in flat 3+1 dimensional spacetime with a time dependent coupling constant which vanishes at $t=0$, like $g_{YM}^2=t^p$. In an analogous quantum mechanics toy model we find that the response is singular. The energy diverges at $t=0$, for a generic state. In addition, if $p>1$ the phase of the wave function has a wildly oscillating behavior, which does not allow it to be continued past $t=0$. A similar effect would make the gauge theory singular as well, though nontrivial effects of renormalization could tame this singularity and allow a smooth continuation beyond $t=0$. The gravity dual in some cases is known to be a time dependent cosmology which exhibits a space-like singularity at $t=0$. Our results, if applicable in the gauge theory for the case of the vanishing coupling, imply that the singularity is a genuine sickness and does not admit a meaningful continuation. When the coupling remains non-zero and becomes small at $t=0$, the curvature in the bulk becomes of order the string scale. The gauge theory now admits a time evolution beyond this point. In this case, a finite amount of energy is produced which possibly thermalizes and leads to a black hole in the bulk.

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arXiv2008

Microstate Dependence of Scattering from the D1-D5 System

We investigate the question of distinguishing between different microstates of the D1-D5 system (with charges Q_1 and Q_5), by scattering with an incoherent beam, composed of a supergravity probe, with central energy E_0 and width (ΔE). The scattering is studied in the dual CFT description in the orbifold limit for finite R, where R is the radius of the circle on which the D1 branes are wrapped. When R(ΔE) >> 1, the absorption cross-section is found to be independent of the microstate and identical to the leading semiclassical answer computed from the naive geometry. For smaller (ΔE), the answer depends on the particular microstate, which we examine for both typical and atypical microstates. We derive an upper bound for the leading correction to the cross-section when 1/R >> ΔE >> (the average energy gap 1/{R [sqrt(Q_1Q_5)]}. For a typical state the bound is proportional to the area of the stretched horizon, [\sqrt(Q_1 Q_5)], up to [log (Q_1Q_5)] terms. Furthermore, when E_0 << (ΔE), the proportionality constant is a pure number independent of all energy scales. Numerical calculations using Lorentzian profiles show that the actual value of the correction is in fact proportional to [sqrt(Q_1Q_5)] without the logarithmic factor. We offer some speculations about how this result can be consistent with a resolution of the naive geometry by higher derivative corrections to supergravity.

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arXiv2007

Gauge Theory Duals of Cosmological Backgrounds and their Energy Momentum Tensors

We revisit Type IIB supergravity backgrounds with null and spacelike singularities with natural gauge theory duals proposed in {\tt hep-th/0602107} and {\tt hep-th/0610053}. We show that for these backgrounds there are always choices of the boundaries of these deformed $AdS_5 \times S^5$ space-times, such that the dual gauge theories live on {\it flat} metrics and have space-time dependent couplings. We present a new time dependent solution of this kind where the effective string coupling is always bounded and vanishes at a spacelike singularity in the bulk, and the space-time becomes $AdS_5 \times S^5$ at early and late times. The holographic energy momentum tensor calculated with a choice of flat boundary is shown to vanish for null backgrounds and to be generically non-zero for time dependent backgrounds.

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arXiv2007

Holography and Cosmological Singularities

Certain null singularities in ten dimensional supergravity have natural holographic duals in terms of Matrix Theory and generalizations of the AdS/CFT correspondence. In many situations the holographic duals appear to be well defined in regions where the supergravity develops singularities. We describe some recent progress in this area.

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arXiv2007

Open String Descriptions of Space-like Singularities in Two Dimensional String Theory

The matrix model formulation of two dimensional string theory has been shown to admit time dependent classical solutions whose closed string duals are geodesically incomplete space-times with space-like boundaries. We investigate some aspects of the dynamics of fermions in one such background. We show that even though the background solution appears pathological, the time evolution of the system is smooth in terms of open string degrees of freedom, viz. the fermions. In particular, an initial state of fermions evolves smoothly into a well defined final state over an infinite open string time interval, while the time perceived by closed strings appears to end abruptly. We outline a method of calculating fermion correlators exactly using symmetry properties. The result for the two point function is consistent with the semiclassical picture.

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arXiv2006

Cosmologies with Null Singularities and their Gauge Theory Duals

We investigate backgrounds of Type IIB string theory with null singularities and their duals proposed in hep-th/0602107. The dual theory is a deformed N=4 Yang-Mills theory in 3+1 dimensions with couplings dependent on a light-like direction. We concentrate on backgrounds which become AdS_5 x S^5 at early and late times and where the string coupling is bounded, vanishing at the singularity. Our main conclusion is that in these cases the dual gauge theory is nonsingular. We show this by arguing that there exists a complete set of gauge invariant observables in the dual gauge theory whose correlation functions are nonsingular at all times. The two-point correlator for some operators calculated in the gauge theory does not agree with the result from the bulk supergravity solution. However, the bulk calculation is invalid near the singularity where corrections to the supergravity approximation become important. We also obtain pp-waves which are suitable Penrose limits of this general class of solutions, and construct the Matrix Membrane theory which describes these pp-wave backgrounds.

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arXiv2006

Time Dependent Cosmologies and Their Duals

We construct a family of solutions in IIB supergravity theory. These are time dependent or depend on a light-like coordinate and can be thought of as deformations of AdS_5 x S^5. Several of the solutions have singularities. The light-like solutions preserve 8 supersymmetries. We argue that these solutions are dual to the N=4 gauge theory in a 3+1 dimensional spacetime with a metric and a gauge coupling that is varying with time or the light-like direction respectively. This identification allows us to map the question of singularity resolution to the dual gauge theory.

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arXiv2006

Matrix Membrane Big Bangs and D-brane Production

We construct Matrix Membrane theory in pp wave backgrounds that have a null linear dilaton in Type IIB string theory. Such backgrounds can serve as toy models of big bang cosmologies. At late times only abelian degrees of freedom survive, and if the Kaluza-Klein modes along one of the directions of the membrane decouple, standard perturbative strings emerge. Near the ``big bang'', non-abelian configurations of fuzzy ellipsoids are present, as in the Type IIA theories. A generic configuration of these shrink to zero volume at late times. However, the Kaluza Klein modes (which can be thought of as states of (p,q) strings in the original IIB theory) can be generically produced in pairs in both pp wave and flat backgrounds in the presence of time dependence. Indeed, if we require that at late times the theory evolves to the perturbative string vacuum, these modes must be prepared in a squeezed state with a thermal distribution at early times.

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arXiv2005

pp Wave Big Bangs: Matrix Strings and Shrinking Fuzzy Spheres

We find pp wave solutions in string theory with null-like linear dilatons. These provide toy models of big bang cosmologies. We formulate Matrix String Theory in these backgrounds. Near the big bang ``singularity'', the string theory becomes strongly coupled but the Yang-Mills description of the matrix string is weakly coupled. The presence of a second length scale allows us to focus on a specific class of non-abelian configurations, viz. fuzzy cylinders, for a suitable regime of parameters. We show that, for a class of pp waves, fuzzy cylinders which start out big at early times dynamically shrink into usual strings at sufficiently late times.

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arXiv2005

Branes wrapping Black Holes

We examine the dynamics of extended branes, carrying lower dimensional brane charges, wrapping black holes and black hole microstates in M and Type II string theory. We show that they have a universal dispersion relation typical of threshold bound states with a total energy equal to the sum of the contributions from the charges. In near-horizon geometries of black holes, these are BPS states, and the dispersion relation follows from supersymmetry as well as properties of the conformal algebra. However they break all supersymmetries of the full asymptotic geometries of black holes and microstates. We comment on a recent proposal which uses these states to explain black hole entropy.

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arXiv2005

Non-trivial 2d space-times from matrices

Solutions of matrix quantum mechanics have been shown to describe time dependent backgrounds in the holographically dual two dimensional closed string theory. We review some recent work dealing with non-trivial space-times which arise in this fashion and discuss aspects of physical phenomena in them.

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arXiv2005

Spacelike boundaries from the c=1 Matrix Model

We find classical solutions of two dimensional noncritical string theory which give rise to geometries with spacelike boundaries, similar to spacetimes with cosmological event horizons. In the c=1 matrix model, these solutions have a representation as simple time dependent configurations. We obtain the causal structure of the resulting spacetimes. Using the macroscopic loop transform, we probe the form of the tachyon condensate in the asymptotic regions.

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