Path integral optimization for TT¯ deformation

Abstract

We use the path integral optimization approach of Caputa, kundu, Miyaji, Takayanagi and Watanabe to find the time slice of geometries dual to vacuum, primary and thermal states in the T T deformed two dimensional CFTs. The obtained optimized geometries actually capture the entire bulk which fits well with the integrability and expected UV-completeness of T T -deformed CFTs. When deformation parameter is positive, these optimized solutions can be reinterpreted as geometries at finite bulk radius, in agreement with a previous proposal by McGough, Mezei and Verlinde. We also calculate the holographic entanglement entropy and quantum state complexity for these solutions. We show that the complexity of formation for the thermofield double state in the deformed theory is UV finite and it depends to the temperature.

$$ T\overline{T} $$ and EE, with implications for (A)dS subregion encodings

“…The on-shell integral for the extremal area then reads 16) and it is easy to check that all the contribution to the entropy comes from z = z c or, equivalently in the x variable, from the endpoints of the entangling region. The entropy evaluates to…”

“…Beyond asymptotic AdS geometries, the causal wedge need not to be smaller than the entanglement wedge. 16 In fact, this is common for the duals of TT deformed theories for a region R which fills up less than half the space. We illustrate this schematically in figure 3.…”

“…Rényi entropies and maximal mixing. We need to evaluate 16) with Z n the partition function on the replicated manifold. This is determined by the VEV of the stress tensor trace, via (2.12)…”

“…Although it is an extraordinarily fruitful case study for quantum gravity, AdS/CFT is neither phenomenologically viable nor generic in string theory, with its special asymptotic boundary and bulk geometry being highly unrealistic. In another line of development, the TT deformation [9][10][11][12] and its generalizations such as [13][14][15][16] enable us to isolate a finite patch of spacetime not intersecting the original boundary [17]. This corresponds to a Dirichlet boundary condition for the metric, and also for additional bulk fields given the prescription [14].…”

Complexity and emergence of warped AdS3 space-time from chiral Liouville action

“…Similar calculations then for the case of warped CFTs or JT deformations could be performed. Recent progress on path-integral optimization for TT has been reported in [104].…”