The procedure of null reduction provides a concrete way of constructing field theories with Galil... more The procedure of null reduction provides a concrete way of constructing field theories with Galilean invariance. We use this to examine Galilean gauge theories, viz. Galilean electrodynamics and Yang-Mills theories in spacetime dimensions 3 and 4. Different non-relativistic conformal symmetries arise in these contexts: Schr{ö}dinger symmetry in $d=3$ and Galilean conformal symmetry in $d=4$. A canonical analysis further reveals that the symmetries enhance to their infinite dimensional versions in phase space and pick up central extensions. In addition, for the Abelian theory, we discuss non-relativistic electro-magnetic duality in $d=3$ and its difference with the $d=4$ version. We also mention some quantum aspects for both Abelian and non-Abelian theories.
We consider holographic theories in bulk (d+1)-dimensions with Lifshitz and hyperscaling violatin... more We consider holographic theories in bulk (d+1)-dimensions with Lifshitz and hyperscaling violating exponents z,θ at finite temperature. By studying shear gravitational modes in the near-horizon region given certain self-consistent approximations, we obtain the corresponding shear diffusion constant on an appropriately defined stretched horizon, adapting the analysis of Kovtun, Son and Starinets. For generic exponents with d-z-θ>-1, we find that the diffusion constant has power law scaling with the temperature, motivating us to guess a universal relation for the viscosity bound. When the exponents satisfy d-z-θ=-1, we find logarithmic behaviour. This relation is equivalent to z=2+d_eff where d_eff=d_i-θ is the effective boundary spatial dimension (and d_i=d-1 the actual spatial dimension). It is satisfied by the exponents in hyperscaling violating theories arising from null reductions of highly boosted black branes, and we comment on the corresponding analysis in that context.
We explore in greater detail our investigations of shear diffusion in hyperscaling violating Lifs... more We explore in greater detail our investigations of shear diffusion in hyperscaling violating Lifshitz theories in arXiv:1604.05092 [hep-th]. This adapts and generalizes the membrane-paradigm-like analysis of Kovtun, Son and Starinets for shear gravitational perturbations in the near horizon region given certain self-consistent approximations, leading to the shear diffusion constant on an appropriately defined stretched horizon. In theories containing a gauge field, some of the metric perturbations mix with some of the gauge field perturbations and the above analysis is somewhat more complicated. We find a similar near-horizon analysis can be obtained in terms of new field variables involving a linear combination of the metric and the gauge field perturbation resulting in a corresponding diffusion equation. Thereby as before, for theories with Lifshitz and hyperscaling violating exponents z, θ satisfying z < 4 − θ in four bulk dimensions, our analysis here results in a similar expression for the shear diffusion constant with power-law scaling with temperature suggesting universal behaviour in relation to the viscosity bound. For z = 4 − θ, we find logarithmic behaviour. Contents 1 Introduction 1 2 Reviewing hyperscaling violating Lifshitz and the shear diffusion constant 4 3 Perturbations in the absence of gauge field: Dilaton gravity 7 4 Perturbations to hyperscaling violating spacetime 11 4.1 Perturbations to hyperscaling violating spacetime: Einstein-Maxwell-dilaton (EMD) theory in 4 dimensions (d = 3
Ghost-spins, 2-level spin-like variables with indefinite norm have been studied in previous work.... more Ghost-spins, 2-level spin-like variables with indefinite norm have been studied in previous work. Here we explore various $N$-level generalizations of ghost-spins. First we discuss a flavoured generalization comprising $N$ copies of the ghost-spin system, as well as certain ghost-spin chains which in the continuum limit lead to 2-dim $bc$-ghost CFTs with $O(N)$ flavour symmetry. Then we explore a symplectic generalization that involves antisymmetric inner products, and finally a ghost-spin system exhibiting $N$ irreducible levels. We also study entanglement properties. In all these cases, we show the existence of positive norm "correlated ghost-spin" states in two copies of ghost-spin ensembles obtained by entangling identical ghost-spins from each copy: these exhibit positive entanglement entropy.
We study extremal surfaces in the Schwarzschild de Sitter spacetime with real mass parameter. We ... more We study extremal surfaces in the Schwarzschild de Sitter spacetime with real mass parameter. We find codim-2 timelike extremal surfaces stretching between the future and past boundaries that pass through the vicinity of the cosmological horizon in a certain limit. These are analogous to the surfaces in arXiv:1711.01107 [hep-th]. We also find spacelike surfaces that never reach the future/past boundaries but stretch indefinitely through the extended Penrose diagram, passing through the vicinity of the cosmological and Schwarzschild horizons in a certain limit. Further, these exhibit interesting structure for de Sitter space (zero mass) as well as in the extremal, or Nariai, limit.
A bstractExtremal black branes upon compactification in the near horizon throat region are known ... more A bstractExtremal black branes upon compactification in the near horizon throat region are known to give rise to AdS2 dilaton-gravity-matter theories. Away from the throat region, the background has nontrivial profile. We interpret this as holographic renormalization group flow in the 2-dim dilaton-gravity-matter theories arising from dimensional reduction of the higher dimensional theories here. The null energy conditions allow us to formulate a holographic c-function in terms of the 2-dim dilaton for which we argue a c-theorem subject to appropriate boundary conditions which amount to restrictions on the ultraviolet theories containing these extremal branes. At the infrared AdS2 fixed point, the c-function becomes the extremal black brane entropy. We discuss the behaviour of this inherited c-function in various explicit examples, in particular compactified nonconformal branes, and compare it with other discussions of holographic c-functions. We also adapt the holographic renormali...
We study dilaton-gravity theories in 2-dimensions obtained by dimensional reduction of higher dim... more We study dilaton-gravity theories in 2-dimensions obtained by dimensional reduction of higher dimensional nonrelativistic theories. Focussing on certain families of extremal charged hyperscaling violating Lifshitz black branes in Einstein-Maxwell-scalar theories with an extra gauge field in 4-dimensions, we obtain AdS 2 backgrounds in the near horizon throats. We argue that these backgrounds can be obtained in equivalent theories of 2-dim dilaton-gravity with an extra scalar, descending from the higher dimensional scalar, and an interaction potential with the dilaton. A simple subcase here is the relativistic black brane in Einstein-Maxwell theory. We then study linearized fluctuations of the metric, dilaton and the extra scalar about these AdS 2 backgrounds. The coefficient of the leading Schwarzian derivative term is proportional to the entropy of the (compactified) extremal black branes.
Two dimensional field theories with Bondi-Metzner-Sachs symmetry have been proposed as duals to a... more Two dimensional field theories with Bondi-Metzner-Sachs symmetry have been proposed as duals to asymptotically flat spacetimes in three dimensions. These field theories are naturally defined on null surfaces and hence are conformal cousins of Carrollian theories, where the speed of light goes to zero. In this paper, we initiate an investigation of anomalies in these field theories. Specifically, we focus on the BMS equivalent of Weyl invariance and its breakdown in these field theories and derive an expression for Weyl anomaly. Considering the transformation of partition functions under this symmetry, we derive a Carrollian Liouville action different from ones obtained in the literature earlier.
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Papers by Kedar Kolekar