arXiv subjects

Dileep P. Jatkar

Publications and source records attributed to Dileep P. Jatkar.

At least 37 records · Page 2Linked to original sources

arXiv2017

SYK Model, Chaos and Conserved Charge

We study the SYK model with complex fermions, in the presence of an all-to-all $q$-body interaction, with a non-vanishing chemical potential. We find that, in the large $q$ limit, this model can be solved exactly and the corresponding Lyapunov exponent can be obtained semi-analytically. The resulting Lyapunov exponent is a sensitive function of the chemical potential $μ$. Even when the coupling $J$, which corresponds to the disorder averaged values of the all to all fermion interaction, is large, values of $μ$ which are exponentially small compared to $J$ lead to suppression of the Lyapunov exponent.

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arXiv2017

Entangled spins and ghost-spins

We study patterns of quantum entanglement in systems of spins and ghost-spins regarding them as simple quantum mechanical toy models for theories containing negative norm states. We define a single ghost-spin as in arXiv:1602.06505 [hep-th] as a 2-state spin variable with an indefinite inner product in the state space. We find that whenever the spin sector is disentangled from the ghost-spin sector (both of which could be entangled within themselves), the reduced density matrix obtained by tracing over all the ghost-spins gives rise to positive entanglement entropy for positive norm states, while negative norm states have an entanglement entropy with a negative real part and a constant imaginary part. However when the spins are entangled with the ghost-spins, there are new entanglement patterns in general. For systems where the number of ghost-spins is even, it is possible to find subsectors of the Hilbert space where positive norm states always lead to positive entanglement entropy after tracing over the ghost-spins. With an odd number of ghost-spins however, we find that there always exist positive norm states with negative real part for entanglement entropy after tracing over the ghost-spins.

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arXiv2017

Ghost-spin chains, entanglement and $bc$-ghost CFTs

We study 1-dimensional chains of ghost-spins with nearest neighbour interactions amongst them, developing further the study of ghost-spins in previous work, defined as 2-state spin variables with indefinite norm. First we study finite ghost-spin chains with Ising-like nearest neighbour interactions: this helps organize and clarify the study of entanglement earlier and we develop this further. Then we study a family of infinite ghost-spin chains with a different Hamiltonian containing nearest neighbour hopping-type interactions. By defining fermionic ghost-spin variables through a Jordan-Wigner transformation, we argue that these ghost-spin chains lead in the continuum limit to the $bc$-ghost CFTs.

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arXiv2016

Extended Supersymmetric BMS$_3$ algebras and Their Free Field Realisations

We study $N=(2,4,8)$ supersymmetric extensions of the three dimensional BMS algebra (BMS$_3$) with most generic possible central extensions. We find that $N$-extended supersymmetric BMS$_3$ algebras can be derived by a suitable contraction of two copies of the extended superconformal algebras. Extended algebras from all the consistent contractions are obtained by scaling left-moving and right-moving supersymmetry generators symmetrically, while Virasoro and R-symmetry generators are scaled asymmetrically. On the way, we find that the BMS/GCA correspondence does not in general hold for supersymmetric systems. Using the $β$-$γ$ and the ${\mathfrak b}$-${\mathfrak c}$ systems, we construct free field realisations of all the extended super-BMS$_3$ algebras.

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arXiv2016

Exploring Lovelock theory moduli space for Schroedinger solutions

We look for Schroedinger solutions in Lovelock gravity in $D > 4$. We span the entire parameter space and determine parametric relations under which the Schroedinger solution exists. We find that in arbitrary dimensions pure Lovelock theories have Schroedinger solutions of arbitrary radius, on a co-dimension one locus in the Lovelock parameter space. This co-dimension one locus contains the subspace over which the Lovelock gravity can be written in the Chern-Simons form. Schroedinger solutions do not exist outside this locus and on this locus they exist for arbitrary dynamical exponent z. This freedom in z is due to the degeneracy in the configuration space. We show that this degeneracy survives certain deformation away from the Lovelock moduli space.

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arXiv2016

Free-field realisations of the BMS$_3$ algebra and its extensions

We construct an explicit realisation of the BMS$_3$ algebra with nonzero central charges using holomorphic free fields. This can be extended by the addition of chiral matter to a realisation having arbitrary values for the two independent central charges. Via the introduction of additional free fields, we extend our construction to the minimally supersymmetric BMS$_3$ algebra and to the nonlinear higher-spin BMS$_3$-W$_3$ algebra. We also describe an extended system that realises both the SU(2) current algebra as well as BMS$_3$ via the Wakimoto representation, though in this case introducing a central extension also brings in new non-central operators.

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arXiv2016

Exact WKB Analysis of N = 2 Gauge Theories

We study N = 2 supersymmetric gauge theories with gauge group SU(2) coupled to fundamental flavours, covering all asymptotically free and conformal cases. We re-derive, from the conformal field theory perspective, the differential equations satisfied by omega deformed instanton partition functions. We confirm their validity at leading order in one of the deformation parameters via a saddle-point analysis of the partition function. In the semi-classical limit we show that these differential equations take a form amenable to exact WKB analysis. We compute the monodromy group associated to the differential equations in terms of deformed and Borel resummed Seiberg-Witten data. For each case, we study pairs of Stokes graphs that are related by flips and pops, and show that the monodromy groups allow one to confirm the Stokes automorphisms that arise as the phase of the deformation parameter is varied. Finally, we relate the Borel resummed monodromies with the traditional Seiberg-Witten variables in the semi-classical limit.

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arXiv2015

Interpolating function and Stokes Phenomena

When we have two expansions of physical quantity around two different points in parameter space, we can usually construct a family of functions, which interpolates the both expansions. In this paper we study analytic structures of such interpolating functions and discuss their physical implications. We propose that the analytic structures of the interpolating functions provide information on analytic property and Stokes phenomena of the physical quantity, which we approximate by the interpolating functions. We explicitly check our proposal for partition functions of zero-dimensional $φ^4$ theory and Sine-Gordon model. In the zero dimensional Sine-Gordon model, we compare our result with a recent result from resurgence analysis. We also comment on construction of interpolating function in Borel plane.

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arXiv2015

Conformal mass in Einstein-Gauss-Bonnet AdS gravity

In this paper, we show that the physical information given by conserved charges for asymptotically AdS spacetimes in Einstein-Gauss-Bonnet AdS gravity is encoded in the electric part of the Weyl tensor. This result generalizes the conformal mass definition by Ashtekar-Magnon-Das (AMD) to a gravity theory with a Gauss-Bonnet term. This proof makes use of the Noether charges obtained from an action renormalized by the addition of counterterms which depend on the extrinsic curvature (Kounterterms). If the asymptotic fall-off behaviour of the Weyl tensor is same as the one considered in the AMD method, then the Kounterterm charges and the AMD charges agree in any dimension.

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arXiv2014

Conformal Mass in AdS gravity

We show that the Ashtekar-Magnon-Das (AMD) mass and other conserved quantities are equivalent to the Kounterterm charges in the asymptotically AdS spacetimes that satisfy the Einstein equations, if we assume the same asymptotic fall-off behavior of the Weyl tensor as considered by AMD. This therefore implies that, in all dimensions, the conformal mass can be directly derived from the bulk action and the boundary terms, which are written in terms of the extrinsic curvature.

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arXiv2013

Stochastic quantization of conformally coupled scalar in AdS

We explore the relation between stochastic quantization and holographic Wilsonian renormalization group flow further by studying conformally coupled scalar in $AdS_{d+1}$. We establish one to one mapping between the radial flow of its double trace deformation and stochastic 2-point correlation function. This map is shown to be identical, up to a suitable field re-definition of the bulk scalar, to the original proposal in arXiv:1209.2242.

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arXiv2012

Stochastic quantization and holographic Wilsonian renormalization group

We study relation between stochastic quantization and holographic Wilsonian renormalization group flow. Considering stochastic quantization of the boundary on-shell actions with the Dirichlet boundary condition for certain $AdS$ bulk gravity theories, we find that the radial flows of double trace deformations in the boundary effective actions are completely captured by stochastic time evolution with identification of the $AdS$ radial coordinate `$r$' with the stochastic time '$t$' as $r=t$. More precisely, we investigate Langevin dynamics and find an exact relation between radial flow of the double trace couplings and 2-point correlation functions in stochastic quantization. We also show that the radial evolution of double trace deformations in the boundary effective action and the stochastic time evolution of the Fokker-Planck action are the same. We demonstrate this relation with a couple of examples: (minimally coupled)massless scalar fields in $AdS_2$ and U(1) vector fields in $AdS_4$.

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arXiv2012

Boundary conditions for SU(2) Yang-Mills on $AdS_4$

We consider SU(2) Yang-Mills theory on $AdS_4$ by imposing various boundary conditions, which correspond to non-trivial deformations of its boundary $CFT$. We obtain classical solutions of Yang-Mills fields up to the first subleading order correction by using small amplitude expansion of the gauge field without considering gravitational back reaction. We also consider SU(2) Yang-Mills instanton solution in $AdS_4$ bulk, and propose a boundary action. It turns out that the boundary theory is the Chern Simons theory with a non-local deformation which has the form similar to the Wilson line. In the limit of the deformation parameter $ρ\rightarrow \infty$, this non-local deformation is suppressed and the boundary theory becomes pure Chern Simons. For large but finite values of $ρ$, this non-local deformation can be treated perturbatively within the Chern-Simon theory.

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arXiv2012

On the Decay of Massive Fields in de Sitter

Interacting massive fields with m > d H/2 in d+1 dimensional de Sitter space are fundamentally unstable. Scalar fields in this mass range can decay to themselves. This process (which is kinematically forbidden in Minkowski space) can lead to an important change to the propagator and the physics of these fields. We compute this decay rate by doing a 1-loop computation for a massive scalar field with a cubic interaction. We resum the 1-loop result by consistently solving the Schwinger-Dyson equations. We also perform an explicit resummation of all chain graphs in the case of the retarded propagator. The decay rate is exponentially suppressed for large m/H and the flat space answer (vanishing decay rate) is reproduced in that limit.

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arXiv2011

BKM superalgebras from counting dyons in N=4 supersymmetric type II compactifications

We study the degeneracy of quarter BPS dyons in N =4 type II compactifications of string theory. We find that the genus-two Siegel modular forms generating the degeneracies of the quarter BPS dyons in the type II theories can be expressed in terms of the genus-two Siegel modular forms generating the degeneracies of quarter BPS dyons in the CHL theories and the heterotic string. This helps us in understanding the algebra structure underlying the degeneracy of the quarter BPS states. The Conway group, Co_1, plays a role similar to Mathieu group, M_{24}, in the CHL models with eta quotients appearing in the place of eta products. We construct BKM Lie superalgebra structures corresponding to Z_N (for N=2,3,4) orbifolds of the type II string compactified on a six-torus.

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arXiv2011

New Massive Gravity and AdS_4 counterterms

We show that the recently proposed DBI extension of new massive gravity emerges naturally as a counterterm in AdS$_4$. The resulting on-shell Euclidean action is independent of the cut-off at zero temperature. We also find that the same choice of counterterm gives the usual area law for the AdS$_4$ Schwarzschild black hole entropy in a cut-off independent manner. The parameter values of the resulting counterterm action correspond to a $c=0$ theory in the context of AdS$_3$/CFT$_2$. We rewrite this theory in terms of the gauge field that is used to recast 3D gravity as a Chern-Simons theory.

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arXiv2011

Geometry and Phase Structure of Non-Relativistic Branes

We use the solution generating technique, the TsT transformation, to obtain new solutions in type II string theory as well as in M-theory. We explicitly work out examples starting with rotating D3 and M2 branes as well as D1-D5-p system. Among a variety of solutions, we find many of them have asymptotic Schrödinger symmetry. We also device a new method of deriving free energy of black brane systems, which is more efficient than the Euclidean action procedure. We test our method on known examples before applying it to new asymptotically Schrödinger backgrounds. We study phase structure of these backgrounds by analysing the free energy thus derived.

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arXiv2010

Non-relativistic metrics from back-reacting fermions

It has recently been pointed out that under certain circumstances the back-reaction of charged, massive Dirac fermions causes important modifications to AdS_2 spacetimes arising as the near horizon geometry of extremal black holes. In a WKB approximation, the modified geometry becomes a non-relativistic Lifshitz spacetime. In three dimensions, it is known that integrating out charged, massive fermions gives rise to gravitational and Maxwell Chern-Simons terms. We show that Schrodinger (warped AdS_3) spacetimes exist as solutions to a gravitational and Maxwell Chern-Simons theory with a cosmological constant. Motivated by this, we look for warped AdS_3 or Schrodinger metrics as exact solutions to a fully back-reacted theory containing Dirac fermions in three and four dimensions. We work out the dynamical exponent in terms of the fermion mass and generalize this result to arbitrary dimensions.

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