67 research outputs found
ABJM theory in Batalin-Vilkovisky formulation
We analyze the quantum ABJM theory on superspace in different
gauges. We study the Batalin-Vilkovisky (BV) formulation for this model. By
developing field/antifield dependent BRST transformation we establish
connection between the two different solutions of the quantum master equation
within the BV formulation.Comment: 9 pages, To appear in Physics Letters
Double Trace Flows and Holographic RG in dS/CFT correspondence
If there is a dS/CFT correspondence, time evolution in the bulk should
translate to RG flows in the dual euclidean field theory. Consequently,
although the dual field is expected to be non-unitary, its RG flows will carry
an imprint of the unitary time evolution in the bulk. In this note we examine
the prediction of holographic RG in de Sitter space for the flow of double and
triple trace couplings in any proposed dual. We show quite generally that the
correct form of the field theory beta functions for the double trace couplings
is obtained from holography, provided one identifies the scale of the field
theory with (i|T|) where T is the `time' in conformal coordinates. For dS(4),
we find that with an appropriate choice of operator normalization, it is
possible to have real n-point correlation functions as well as beta functions
with real coefficients. This choice leads to an RG flow with an IR fixed point
at negative coupling unlike in a unitary theory where the IR fixed point is at
positive coupling. The proposed correspondence of Sp(N) vector models with de
Sitter Vasiliev gravity provides a specific example of such a phenomenon. For
dS(d+1) with even d, however, we find that no choice of operator normalization
exists which ensures reality of coefficients of the beta-functions as well as
absence of n-dependent phases for various n-point functions, as long as one
assumes real coupling constants in the bulk Lagrangian.Comment: 18 pages, no figures; (v2) minor typos fixed, references adde
dS/CFT at uniform energy density and a de Sitter "bluewall"
We describe a class of spacetimes that are asymptotically de Sitter in the
Poincare slicing. Assuming that a dS/CFT correspondence exists, we argue that
these are gravity duals to a CFT on a circle leading to uniform energy-momentum
density, and are equivalent to an analytic continuation of the Euclidean AdS
black brane. These are solutions with a complex parameter which then gives a
real energy-momentum density. We also discuss a related solution with the
parameter continued to a real number, which we refer to as a de Sitter
"bluewall". This spacetime has two asymptotic de Sitter universes and Cauchy
horizons cloaking timelike singularities. We argue that the Cauchy horizons
give rise to a blue-shift instability.Comment: Latex, 13pgs, 2 figs. v2: 14pgs, published version, some rephrasing
of language in terms of Euclidean CFT on a circle, more elaborate discussion
on blueshif
TIME DEPENDENT HOLOGRAPHY
One of the most important results emerging from string theory is the gauge gravity duality (AdS/CFT correspondence) which tells us that certain problems in particular gravitational backgrounds can be exactly mapped to a particular dual gauge theory a quantum theory very similar to the one explaining the interactions between fundamental subatomic particles. The chief merit of the duality is that a difficult problem in one theory can be mapped to a simpler and solvable problem in the other theory. The duality can be used both ways.
Most of the current theoretical framework is suited to study equilibrium systems, or systems where time dependence is at most adiabatic. However in the real world, systems are almost always out of equilibrium. Generically these scenarios are described by quenches, where a parameter of the theory is made time dependent. In this dissertation I describe some of the work done in the context of studying quantum quench using the AdS/CFT correspondence. We recover certain universal scaling type of behavior as the quenching is done through a quantum critical point. Another question that has been explored in the dissertation is time dependence of the gravity theory. Present cosmological observations indicate that our universe is accelerating and is described by a spacetime called de-Sitter(dS). In 2011 there had been a speculation over a possible duality between de-Sitter gravity and a particular field theory (Euclidean SP(N) CFT). However a concrete realization of this proposition was still lacking. Here we explicitly derive the dS/CFT duality using well known methods in field theory. We discovered that the time dimension emerges naturally in the derivation. We also describe further applications and extensions of dS/CFT
Integrability Lost
It is known that classical string dynamics in pure AdS_5\times S^5 is
integrable and plays an important role in solvability. This is a deep and
central issue in holography. Here we investigate similar classical
integrability for a more realistic confining background and provide a negative
answer. The dynamics of a class of simple string configurations in AdS soliton
background can be mapped to the dynamics of a set of non-linearly coupled
oscillators. In a suitable limit of small fluctuations we discuss a
quasi-periodic analytic solution of the system. However numerics indicates
chaotic behavior as the fluctuations are not small. Integrability implies the
existence of a regular foliation of the phase space by invariant manifolds. Our
numerics shows how this nice foliation structure is eventually lost due to
chaotic motion. We also verify a positive Lyapunov index for chaotic orbits.
Our dynamics is roughly similar to other known non-integrable coupled
oscillators systems like Henon-Heiles equations.Comment: Acknowledged grant
Modular crossings, OPE coefficients and black holes
In (1+1)-d CFTs, the 4-point function on the plane can be mapped to the
pillow geometry and thereby crossing symmetry gets translated into a modular
property. We use these modular features to derive a universal asymptotic
formula for OPE coefficients in which one of the operators is averaged over
heavy primaries. The coarse-grained heavy channel then reproduces features of
the gravitational 2-to-2 S-matrix which has black holes as their intermediate
states.Comment: 6 pages and a pillow; v3 : approximates published versio
Monstrous entanglement
The Monster CFT plays an important role in moonshine and is also conjectured
to be the holographic dual to pure gravity in AdS3. We investigate the
entanglement and Renyi entropies of this theory along with other extremal CFTs.
The Renyi entropies of a single interval on the torus are evaluated using the
short interval expansion. Each order in the expansion contains closed form
expressions of the modular parameter. The leading terms in the q-series are
shown to precisely agree with the universal corrections to Renyi entropies at
low temperatures. Furthermore, these results are shown to match with bulk
computations of Renyi entropy using the one-loop partition function on
handlebodies. We also explore some features of Renyi entropies of two intervals
on the plane.Comment: 41 pages, 4 figures; v2: typos corrected, approximates published
versio
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