We introduce a new optimization procedure for Euclidean path integrals, which compute wave functionals in conformal field theories (CFTs). optimize the background metric space on integration is performed. Equivalently, this interpreted as position-dependent UV cutoff. For two-dimensional CFT vacua, we find optimized given by that of hyperbolic space, and interpret continuous limit conjectured relation between tensor networks Anti--de Sitter (AdS)/conformal theory (CFT) correspondence....

A bstract We propose an optimization procedure for Euclidean path-integrals that evaluate CFT wave functionals in arbitrary dimensions. The is performed by minimizing certain functional, which can be interpreted as a measure of computational complexity, with respect to background metrics the path-integrals. In two dimensional CFTs, this functional given Liouville action. also formulate higher CFTs and, various examples, find optimized hyperbolic coincide time slices expected gravity duals....

We study the two-point function for fermionic operators in a class of strongly coupled systems using gauge-gravity correspondence. The gravity description includes gauge field and dilaton which determines coupling potential energy. Extremal black brane solutions this system typically have vanishing entropy. By analyzing charged fermion these extremal backgrounds we calculate corresponding boundary operator. find that some region parameter space it is Fermi liquid type. Outside no...

We calculate the four point correlation function for scalar perturbations in canonical model of slow-roll inflation. work leading approximation where calculation can be done de Sitter space. Our uses techniques drawn from AdS/CFT correspondence to find wave at late times and then it. The answer we get agrees with an earlier result literature, obtained using different methods. analysis reveals a subtlety regard Ward identities conformal invariance, which arises space has no analogue AdS This...

Using symmetry considerations, we derive Ward identities which relate the three point function of scalar perturbations produced during inflation to four function, in a particular limit. The derivation assumes approximate conformal invariance, and conditions for slow roll approximation, but is otherwise model independent. allow us deduce that must be suppressed general, being same order magnitude as model. They also fix terms upto one constant argue generically suppressed. Our approach based...

A bstract In this work, we formulate a path-integral optimization for two dimensional conformal field theories perturbed by relevant operators. We present several evidences how mechanism works, based on calculations in free as well general arguments of RG flows theories. Our is performed minimizing the complexity functional that depends metric and also couplings. Then, compute optimal perturbatively find it agrees with time slice hyperbolic scalar AdS/CFT correspondence. Last but not least,...

Extremal black branes are of interest because they correspond to the ground states field theories at finite charge density in gauge/gravity duality. The geometry such a brane need not be translationally invariant spatial directions along which it extends. A less restrictive requirement is that homogeneity, still allows points related each other by symmetries. In this paper, we find large new classes homogeneous but anisotropic extremal horizons, could naturally arise dual pairs. 4+1...

We consider a system consisting of 5 dimensional gravity with negative cosmological constant coupled to massless scalar, the dilaton. construct black brane solution which arises when dilaton satisfies linearly varying boundary conditions in asymptotically AdS region. The geometry this breaks rotational symmetry while preserving translational invariance and corresponds an anisotropic phase system. Close extremality, where anisotropy is big compared temperature, some components viscosity...

A bstract Classifying the zero-temperature ground states of quantum field theories with finite charge density is a very interesting problem. Via holography, this problem mapped to classification extremal charged black brane geometries anti-de Sitter asymptotics. In recent paper [1], we proposed Bianchi near-horizon in five dimensions, case where they are homogeneous but, general, anisotropic. Here, extend our study two directions: show that attractors can lead new phases, and generalize...

We derive the general Ward identities for scale and special conformal transformations in theories of single field inflation. Our analysis is model independent based on symmetry considerations alone. The we obtain are valid to all orders slow roll expansion. For transformations, include a term which non-linear fields that arises due compensating spatial reparametrization. Some observational consequences also discussed.

A bstract Focussing on theories for which the higher derivative terms are considered as small corrections in Lagrangian to Einstein’s two-derivative theory of general relativity (GR), we prove classical version covariant entropy bound (also known Bousso bound) arbitrary diffeomorphism invariant gravitational theories. Even if treated perturbatively, provide instances specific configurations they can potentially violate bound. To tackle this obstruction, propose a modification that...

A bstract We construct a proof of the second law thermodynamics in an arbitrary diffeomorphism invariant theory gravity working within approximation linearized dynamical fluctuations around stationary black holes. achieve this by establishing existence entropy current defined on horizon dynamically perturbed hole such theories. By construction, has non-negative divergence, suggestive mechanism for to approach final equilibrium configuration via production as well spatial flow it null...

We propose an entropy current for dynamical black holes in a theory with arbitrary four derivative corrections to Einstein's gravity, linearized around stationary hole. The Einstein-Gauss-Bonnet is special case of the class theories that we consider. Within our approximation, construction allows us write down completely local version second law hole thermodynamics, presence higher considered here. This ultra-local, stronger form generalization weaker form, applicable total entropy,...

A bstract We consider diffeomorphism invariant theories of gravity with arbitrary higher derivative terms in the Lagrangian as corrections to leading two theory Einstein’s general relativity. construct a proof zeroth law black hole thermo-dynamics such theories. assume that stationary solution an can be obtained by starting corresponding relativity and correcting it order perturbative expansion coupling constants Lagrangian. prove surface remains constant on its horizon when computed for...

We construct classes of smooth metrics which interpolate from Bianchi attractor geometries Types II, III, VI and IX in the IR to Lifshitz or $AdS_2 \times S^3$ UV. While we do not obtain these as solutions Einstein gravity coupled a simple matter field theory, show that sector stress-energy required support (via equations) does satisfy weak, therefore also null, energy condition. Since can turn be connected $AdS_5$ spacetime, our results there is no barrier, at least level conditions, for...

In classical general relativity described by Einstein-Hilbert gravity, black holes behave as thermodynamic objects. particular, the laws of hole mechanics can be interpreted thermodynamics. The first law extends to higher derivative theories via Noether charge construction Wald. One also expects statement second law, which in theory owes Hawking's area theorem, extend theories. To argue for this however one needs a notion entropy dynamical holes, does not provide. We propose such an function...

A bstract This work extends the proof of a local version linearized second law involving an entropy current with non-negative divergence by including arbitrary non-minimal coupling scalar and U(1) gauge fields gravity. In recent works, construction to prove rested on important assumption about possible matter couplings gravity: corresponding stress tensor was assumed satisfy null energy conditions. However, condition can be violated, even classically, when gravity is considered. Considering...

We study the surface transport properties of stationary localized configurations relativistic fluids to first two non-trivial orders in a derivative expansion. By demanding that these finite lumps fluid are described by thermal partition function with arbitrary background metric and gauge fields, we able find several constraints among coefficients. At leading order, besides recovering thermodynamics, obtain generalization Young-Laplace equation for surfaces, considering temperature...

A bstract De-Sitter(dS) space allows for a generalized class of vacua, known as α –vacua, described by some parameters. The Bunch-Davies (BD) vacuum is point in this parameter space. cosmological correlation function BD four dimensions and can be interpreted CFT 3 certain operators. However, the α– vacua takes much more complicated form. In paper, we give simple prescription to compute terms vacuum. We also show that related three-dimensional functions if relax requirement consistency with...

A bstract We construct an entropy current and establish a local version of the classical second law thermodynamics for dynamical black holes in Chern-Simons (CS) theories gravity. work chosen set Gaussian null coordinates assume dynamics to be small perturbations around Killing horizon. In explicit examples both purely gravitational mixed gauge gravity CS (2 + 1) (4 1)-dimensions, is obtained by studying off-shell structure equations motion evaluated on For theory dimensions, we argue that...

A bstract We study the conformal invariance of inflationary non-Gaussianities associated with scalar fluctuations in a non-Bunch-Davies initial state, known as α -vacuum, single-field slow-roll inflation. The -vacuum is one-parameter family states, including Bunch-Davies one, that preserves symmetry dynamics nearly de-Sitter space-time. Working within leading approximation, we compute four-point correlator (the trispectrum) using in-in formalism. check Ward identities are met between three...

Developing on a recent work localized bubbles of ordinary relativistic fluids, we study the comparatively richer leading order surface physics superfluids, coupled to an arbitrary stationary background metric and gauge field in 3 + 1 2 dimensions. The analysis is performed with help Euclidean effective action one lower dimension, written terms superfluid Goldstone mode, shape-field (characterizing bubble) fields. We find new ideal constitutive relations surface, both parity-even parity-odd...

In this article we report on a preliminary study, {\it via} Holography, of infrared fixed points in putative strongly coupled SU$(N_c)$ gauge theory, with $N_f$ fundamental matter, the presence additional fields sector, e.g. density or magnetic field. an inherently effective} bottom up} approach, work simple system: Einstein-gravity negative cosmological constant, to Dirac-Born-Infeld (DBI) matter. We obtain class exact solutions, dual candidate grounds states (IR), scaling ansatz for...