Arbitrary Conformal Dimension Research Articles

Conformal super Virasoro algebra: Matrix model and quantum deformed algebra

In this paper, we construct the super Virasoro algebra with an arbitrary conformal dimension [Formula: see text] from the generalized [Formula: see text]-deformed quantum algebra and investigate the [Formula: see text]-deformed super Virasoro algebra with the particular conformal dimension [Formula: see text] Furthermore, we perform the [Formula: see text]-conformal Virasoro [Formula: see text]-algebra, the [Formula: see text]-conformal super Virasoro [Formula: see text]-algebra ([Formula: see text]-even) and discuss a toy model for the [Formula: see text]-conformal Virasoro constraints and [Formula: see text]-conformal super Virasoro constraints. Besides, we generalized the notion of the [Formula: see text]-elliptic Hermitian matrix model with an arbitrary conformal dimension [Formula: see text]. Finally, we deduce relevant particular cases generated by quantum algebras known in the literature.

Localized states in global AdS space

We construct both local states and scattering states with finite energy in global AdS by inserting properly regularized operators in the CFT of arbitrary conformal dimension $(\Delta)$ at an instant of time. We give the state fixed angular momentum $(\ell)$ by integrating the result over a sphere with appropriate spherical harmonics. The energy of the states and their angular resolution is computed with CFT operator methods and is independent of having an AdS interpretation. In the semiclassical limit of large conformal dimension operators, these correspond to single particles localized within subAdS scales with width $1/\sqrt{\Delta}$ in AdS units, whose subsequent evolution is controlled by bulk geodesics. Our construction allows us to place a particle in any desired geodesic. For radial geodesics, we show that the amplitude to produce the desired state can be thought of as a regularized tunneling amplitude from the boundary to the radial turning point of the radial geodesic, while for other geodesics we argue that the insertion is at the outermost radial turning point of the corresponding geodesic.

R ( p , q ) -deformed conformal Virasoro algebra

This paper addresses an R(p,q)-deformed conformal Virasoro algebra with an arbitrary conformal dimension Δ. Well-known deformations constructed in the literature are deduced as particular cases. Then, the special case of the conformal dimension Δ = 1 is elucidated for its interesting properties. The R(p,q)− KdV equation, associated with the deformed Virasoro algebra, is also derived and discussed. Finally, the (p, q)-deformed energy-momentum tensor, consistent with the central extension term, is computed and analyzed.

Quantum quenches of holographic plasmas

We employ holographic techniques to study quantum quenches at finite temperature, where the quenches involve varying the coupling of the boundary theory to a relevant operator with an arbitrary conformal dimension $2\leq\D\leq4$. The evolution of the system is studied by evaluating the expectation value of the quenched operator and the stress tensor throughout the process. The time dependence of the new coupling is characterized by a fixed timescale and the response of the observables depends on the ratio of the this timescale to the initial temperature. The observables exhibit universal scaling behaviours when the transitions are either fast or slow, i.e. when this ratio is very small or very large. The scaling exponents are smooth functions of the operator dimension. We find that in fast quenches, the relaxation time is set by the thermal timescale regardless of the operator dimension or the precise quenching rate.

Holographic real-time nonrelativistic correlators at zero and finite temperature

We compute a variety of two and three-point real-time correlation functions for a strongly-coupled non-relativistic field theory. We focus on the theory conjectured to be dual to the Schr\"{o}dinger-invariant gravitational spacetime introduced by Balasubramanian, McGreevy, and Son, but our methods apply to a large class of non-relativistic theories. At zero temperature, we obtain time-ordered, retarded, and Wightman non-relativistic correlators for scalar operators of arbitrary conformal dimension directly in field theory by applying a certain lightlike Fourier transform to relativistic conformal correlators, and we verify that non-relativistic AdS/CFT reproduces the results. We compute thermal two and three-point real-time correlators for scalar operators dual to scalar fields in the black hole background which is the finite temperature generalization of the Schr\"{o}dinger spacetime. This is done by first identifying thermal real-time bulk-to-boundary propagators, which combined with Veltman's circling rules, yield two and three-point correlators. The two-point correlators we obtain satisfy the Kallen-Lehmann relations. We also give retarded and time-ordered three-point correlators.

Light-cone formulation of conformal field theory adapted to AdS/CFT correspondence

Light-cone formulation of conformal field theory in space–time of arbitrary dimension is developed. Conformal fundamental and shadow fields with arbitrary conformal dimension and arbitrary spin are studied. Representation of conformal algebra generators on space of conformal fundamental and shadow fields in terms of spin operators which enter in light-cone gauge formulation of field dynamics in AdS space is found. As an example of application of light-cone formalism we discuss AdS/CFT correspondence for massive arbitrary spin AdS fields and corresponding boundary CFT fields at the level of two point function.

General graviton exchange graph for four-point functions in the AdS/CFT correspondence

In this note we explicitly compute the graviton exchange graph for scalar fields with arbitrary conformal dimension \Delta in arbitrary spacetime dimension d. This results in an analytical function in \Delta as well as in d.

Hermitian versus anti-hermitian one-matrix models and their hierarchies

Building on a recent work of Č. Crnković, M. Douglas and G. Moore, a study of multi-critical multi-cut one-matrix models and their associated sl(2, C ) integrable hirarchies, is further pursued. The double-scaling limits of hermitian matrix models with different scaling ansätze, lead to the KdV hierarchy, to the modified KdV hierarchy and part of the non-linear Schrödinger hierarchy. Instead, the anti-hermitian matrix model, in the 2-arc sector, results in the Zakharov-Shabat hierarchy, which contains both KdV and mKdV as reductions. For all the hierarchies it is found that the Virasoro constraints act on the associated τ-functions. Whereas it is known that the ZS and KdV models lead to the Virasoro constraints of an sl(2, C ) vacuum, we find that the mKdV model leads to the Virasoro constraints of a highest-weight state with arbitrary conformal dimension.