arXiv subjects
Publications and source records attributed to K. Narayan.
We review aspects of certain time-dependent deformations of $AdS/CFT$ containing cosmological singularities and their gauge theory duals. Towards understanding these solutions better, we explore similar singular deformations of de Sitter space and argue that these solutions are constrained, possibly corresponding to specific initial conditions.
We explore string/M-theory constructions of holographic theories with Lifshitz scaling exponent $z$ and hyperscaling violation exponent $θ$, finding a range of $z,θ$-values. Some of these arise as effective metrics from dimensional reduction of certain kinds of null deformations of $AdS$ spacetimes appearing in the near horizon geometries of extremal D3-, M2- and M5-brane theories. The $AdS_5$ solution in particular gives rise to $θ=1$ in $d=2$ (boundary) space dimensions. Other solutions arise as the IIA D2- and D4-brane solutions with appropriate null deformations, and we discuss the phase structure of these systems.
Following arXiv:1005.3291 [hep-th], we discuss certain lightlike deformations of $AdS_5\times X^5$ in Type IIB string theory sourced by a lightlike dilaton $Φ(x^+)$ dual to the N=4 super Yang-Mills theory with a lightlike varying gauge coupling. We argue that in the case where the $x^+$-direction is noncompact, these solutions describe anisotropic 3+1-dim Lifshitz-like systems with a potential in the $x^+$-direction generated by the lightlike dilaton. We then describe solutions of this sort with a linear dilaton. This enables a detailed calculation of 2-point correlation functions of operators dual to bulk scalars and helps illustrate the spatial structure of these theories. Following this, we discuss a nongeometric string construction involving a compactification along the $x^+$-direction of this linear dilaton system. We also point out similar IIB axionic solutions. Similar bulk arguments for $x^+$-noncompact can be carried out for deformations of $AdS_4\times X^7$ in M-theory.
In arXiv:0909.4731 [hep-th], we argued that the free string lightcone Schrodinger wavefunctional in the vicinity of null Kasner-like cosmological singularities has nonsingular time-dependence if the Kasner exponents satisfy certain relations. These backgrounds are anisotropic plane waves with singularities. We first show here that only certain singularities admit a Rosen-Kasner frame with exponents satisfying relations leading to a wavefunctional with nonsingular time-dependence. Then we build on the (Rosen) description further and study various physical observables for a time-dependent harmonic oscillator toy model and then the free string, reconciling this with the corresponding description in the conventional plane wave variables. We find that observables containing no time derivatives are identical in these variables while those with time derivatives are different. Various free string observables are still divergent, perhaps consistent with string oscillator states becoming light in the vicinity of the singularity.
We describe solutions of 10-dimensional supergravity comprising null deformations of $AdS_5\times S^5$ with a scalar field, which have $z=2$ Lifshitz symmetries. The bulk Lifshitz geometry in 3+1-dimensions arises by dimensional reduction of these solutions. The dual field theory in this case is a deformation of the N=4 super Yang-Mills theory. We discuss the holographic 2-point function of operators dual to bulk scalars. We further describe time-dependent (cosmological) solutions which have anisotropic Lifshitz scaling symmetries. We also discuss deformations of $AdS\times X$ in 11-dimensional supergravity, which are somewhat similar to the solutions above. In some cases here, we expect the field theory duals to be deformations of the Chern-Simons theories on M2-branes stacked at singularities.
We continue exploring free strings in the background of null Kasner-like cosmological singularities, following arXiv:0904.4532 [hep-th]. We study the free string Schrodinger wavefunctional along the lines of arXiv:0807.1517 [hep-th]. We find the wavefunctional to be nonsingular in the vicinity of singularities whose Kasner exponents satisfy certain relations. We compare this with the description in other variables. We then study certain regulated versions of these singularities where the singular region is replaced by a substringy but nonsingular region and study the string spectra in these backgrounds. The string modes can again be solved for exactly, giving some insight into how string oscillator states get excited near the singularity.
We investigate nonsupersymmetric $\BC^4/\BZ_N$ orbifold singularities using their description in terms of the string worldsheet conformal field theory and its close relation with the toric geometry description of these singularities and their possible resolutions. Analytic and numerical study strongly suggest the absence of nonsupersymmetric Type II terminal singularities (i.e. with no marginal or relevant blowup modes) so that there are always moduli or closed string tachyons that give rise to resolutions of these singularities, although supersymmetric and Type 0 terminal singularities do exist. Using gauged linear sigma models, we analyze the phase structure of these singularities, which often involves 4-dimensional flip transitions, occurring between resolution endpoints of distinct topology. We then discuss 4-dim analogs of unstable conifold-like singularities that exhibit flips, in particular their Type II GSO projection and the phase structure. We also briefly discuss aspects of M2-branes stacked at such singularities and nonsupersymmetric $AdS_4\times S^7/\BZ_N$ backgrounds.
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.
We construct cosmological spacetimes with null Kasner-like singularities as purely gravitational solutions with no other background fields turned on. These can be recast as anisotropic plane-wave spacetimes by coordinate transformations. We analyse string quantization to find the spectrum of string modes in these backgrounds. The classical string modes can be solved for exactly in these time-dependent backgrounds, which enables a detailed study of the near singularity string spectrum, (time-dependent) oscillator masses and wavefunctions. We find that for low lying string modes(finite oscillation number), the classical near-singularity string mode functions are non-divergent for various families of singularities. Furthermore, for any infinitesimal regularization of the vicinity of the singularity, we find a tower of string modes of ultra-high oscillation number which propagate essentially freely in the background. The resulting picture suggests that string interactions are non-negligible near the singularity.
A quarter-BPS dyon in $\mathcal{N}=4$ super Yang-Mills theory is generically `decadent' in that it is stable only in some regions of the moduli space and decays on submanifolds in the moduli space. Using this fact, and from the degeneracy of the system close to the decay, a new derivation for the degeneracy of such dyons is given. The degeneracy obtained from these very simple physical considerations is in precise agreement with the results obtained from index computations in all known cases. Similar considerations apply to dyons in $\mathcal{N}=2$ gauge theories. The relation between the $\mathcal{N} =4 $ field theory dyons and those counted by the Igusa cusp form in toroidally compactified heterotic string is elucidated.
We use the low energy effective $U(1)^r$ action on the Coulomb branch of ${\cal N}=4$ super Yang-Mills theory to construct approximate field configurations for solitonic dyons in these theories, building on the brane prong description developed in hep-th/0101114. This dovetails closely with the corresponding description of these dyons as string webs stretched between D-branes in the transverse space. The resulting picture within these approximations shows the internal structure of these dyons (for fixed asymptotic charges) to be molecule-like, with multiple charge cores held together at equilibrium separations, which grow large near lines of marginal stability. Although these techniques do not yield a complete solution for the spatial structure (i.e. all core sizes and separations) of large charge multicenter dyons in high rank gauge theories, approximate configurations can be found in specific regions of moduli space, which become increasingly accurate near lines of marginal stability. We also discuss string webs with internal faces from this point of view.
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.
We study the half-BPS mesonic chiral ring of the N=1 superconformal quiver theories arising from N D3-branes stacked at Y^pq and L^abc Calabi-Yau conical singularities. We map each gauge invariant operator represented on the quiver as an irreducible loop adjoint at some node, to an invariant monomial, modulo relations, in the gauged linear sigma model describing the corresponding bulk geometry. This map enables us to write a partition function at finite N over mesonic half-BPS states. It agrees with the bulk gravity interpretation of chiral ring states as cohomologically trivial giant gravitons. The quiver theories for L^aba, which have singular base geometries, contain extra operators not counted by the naive bulk partition function. These extra operators have a natural interpretation in terms of twisted states localized at the orbifold-like singularities in the bulk.
We explore the phase structure induced by closed string tachyon condensation of toric nonsupersymmetric conifold-like singularities described by an integral charge matrix $Q=(n_1 n_2 -n_3 -n_4), n_i>0, \sum_i Q_i\neq 0$, initiated in hep-th/0510104. Using gauged linear sigma model renormalization group flows and toric geometry techniques, we see a cascade-like phase structure containing decays to lower order conifold-like singularities, including in particular the supersymmetric conifold and the $Y^{pq}$ spaces. This structure is consistent with the Type II GSO projection obtained previously for these singularities. Transitions between the various phases of these geometries include flips and flops.
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.
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.
Following the analysis of tachyons and orbifold flips described in hep-th/0412337, we study nonsupersymmetric analogs of the supersymmetric conifold singularity and show using their toric geometry description that they are nonsupersymmetric orbifolds of the latter. Using linear sigma models, we see that these are unstable to localized closed string tachyon condensation and exhibit flip transitions between their two small resolutions (involving 2-cycles), in the process mediating mild dynamical topology change. Our analysis shows that the structure of these nonsupersymmetric conifolds as quotients of the supersymmetric conifold obstructs the 3-cycle deformation of such singularities, suggesting that these nonsupersymmetric conifolds decay by evolving towards their stable small resolutions.
In this paper we study various cosmological solutions for a D3/D7 system directly from M-theory with fluxes and M2-branes. In M-theory, these solutions exist only if we incorporate higher derivative corrections from the curvatures as well as G-fluxes. We take these corrections into account and study a number of toy cosmologies, including one with a novel background for the D3/D7 system whose supergravity solution can be completely determined. This new background preserves all the good properties of the original model and opens up avenues to investigate cosmological effects from wrapped branes and brane-antibrane annihilation, to name a few. We also discuss in some detail semilocal defects with higher global symmetries, for example exceptional ones, that could occur in a slightly different regime of our D3/D7 model. We show that the D3/D7 system does have the required ingredients to realise these configurations as non-topological solitons of the theory. These constructions also allow us to give a physical meaning to the existence of certain underlying homogeneous quaternionic Kahler manifolds.