A Solvable Irrelevant Deformation of $AdS_3/CFT_2$ (1707.05800v1)

Abstract: Recently we proposed a universal solvable irrelevant deformation of $AdS_3/CFT_2$ duality, which leads in the ultraviolet to a theory with a Hagedorn entropy [1]. In this note we provide a worldsheet description of this theory as a coset CFT, and compare its spectrum to the field theory predictions of [2,3].

• The paper introduces a solvable irrelevant deformation via a worldsheet coset CFT approach that unifies IR CFT behavior with UV Hagedorn growth.
• It compares single trace and double trace deformations, highlighting how a universal single trace operator modifies the AdS3 bulk geometry.
• The findings provide insights into spectral properties and entropy transitions, linking long string physics to black hole thermodynamics.

A Solvable Irrelevant Deformation of AdS/CFT

The paper examines a proposed solvable irrelevant deformation of the AdS/CFT duality, emphasizing the approach through a worldsheet description based on coset Conformal Field Theories (CFTs). The analysis explores the spectrum, energy characteristics, and broader implications of these deformed theories.

The research continues the investigation into a specific irrelevant deformation of string theory on AdS$_3$, motivated by earlier works on two-dimensional CFT perturbations. Specifically, the perturbation by a dimension (2,2) operator relates to the $T\bar{T}$ deformation, speculated to be exactly solvable and exhibiting a smooth entropy spectrum transitioning from CFT in the infrared (IR) to Hagedorn growth in the ultraviolet (UV).

A central component of this analysis is the comparison between single trace and double trace deformations in string theory. Notably, the single trace deformation addressed here modifies the bulk's local geometry, potentially offering deeper insights than previous models. This deformation is characterized by introducing a single trace operator universal across all vacua of string theory on AdS$_3$, contrasting with the double trace deformations, which modify boundary conditions for bulk fields.

The paper employs a worldsheet coset CFT approach to describe this string theory deformation, which involves null gauging techniques in a 10+2 dimensional background. Through this mathematical construct, the authors articulate the emergence of an asymptotically linear dilaton geometry that interpolates from near-horizon AdS$_3$ for both strings and fivebranes in the IR towards a linear dilaton geometry representing only fivebranes in the UV domain.

Key insights into the spectrum include:

• The paper finds that spectral properties at high energies agree with expectations for the Bekenstein-Hawking entropy related to black holes within deformed geometries.
• The analysis reveals that perturbative excitations within this setup exhibit continuous spectra similar to long string solutions in undeformed backgrounds, which supports previous conjectures about black hole/string transitions.
• Furthermore, the entropy transitions illustrate both the CFT-like behavior in the IR and a thermodynamic approach resembling Hagedorn phenomena at higher energy levels.

In terms of implications, the results reinforce a framework where long strings provide a bridge to black hole physics, complementing broader insights into holography and non-perturbative string theory. The research underlines the utility of coset CFTs in providing exact solutions and suggests future avenues to incorporate non-supersymmetric backgrounds and other complex holographic models.

Overall, the findings contribute to a robust understanding of deformation in holographic duality and string theory, with potential ramifications across quantum gravity and theoretical physics exploring the limits of solvable deformations. Further exploration could build on this groundwork to assess detailed observables and test boundary correspondences within different holographic scenarios.