Deforming the D1D5 CFT away from the orbifold point

Self Cite

Abstract:We consider the issue of thermalization in the D1D5 CFT. Thermalization is expected to correspond to the formation of a black hole in the dual gravity theory. We start from the orbifold point, where the theory is essentially free, and does not thermalize. In earlier work it was noted that there was no clear thermalization effect when the theory was deformed off the orbifold point to first order in the relevant twist perturbation. In this paper we consider the deformation to second order in the twist, where we do find effects that can cause thermalization of an initial perturbation. We consider a 1-loop process where two untwisted copies of the CFT are twisted to one copy and then again untwisted to two copies. We start with a single oscillator excitation on the initial CFT, and compute the effect of the two twists on this state. We find simple approximate expressions for the Bogoliubov coefficients and the behavior of the single oscillator excitation in the continuum limit, where the mode numbers involved are taken to be much larger than unity. We also prove a number of useful relationships valid for processes with an arbitrary number of twist insertions.

Section: Introductionmentioning

confidence: 99%

“…In the intermediate regions we have a single doubly-wound component string in the state |χ(w 1 , w 2 ) . This state was computed in [25] and is not used here.…”

Section: Introductionmentioning

confidence: 99%

One-loop transition amplitudes in the D1D5 CFT

Carson

Hampton

Mathur

2017

Self Cite

“…The reason for this seemingly unreasonable effectiveness was clarified in [14] (see also [15][16][17] for related earlier works): for CFTs with a large central charge (corresponding to the semi-classical limit on the gravity side) and a sparse light spectrum, the Cardy regime extends all the way down to where the condition L + 0 + L − 0 ≥ c 12 is satisfied. This behavior puts constraints on the precise nature of 2d CFTs potentially dual to AdS 3 theories of gravity, examples of which include symmetric orbifolds [14,[17][18][19][20][21] and extremal CFTs [22,23]. Other CFTs potentially dual to AdS 3 gravity have recently been discussed in [24] The key property responsible for the existence of a simple and elegant formula like (1.1) is modular invariance.…”

Section: Jhep06(2016)014mentioning

confidence: 99%

Warped AdS3 black holes in higher derivative gravity theories

Detournay¹,

Douxchamps²,

Ng³

et al. 2016

We consider warped AdS 3 black holes in generic higher derivatives gravity theories in 2+1 dimensions. The asymptotic symmetry group of the phase space containing these black holes is the semi-direct product of a centrally extended Virasoro algebra and an affine u(1) Kac-Moody algebra. Previous works have shown that in some specific theories, the entropy of these black holes agrees with a Cardy-like entropy formula derived for warped conformal field theories. In this paper, we show that this entropy matching continues to hold for the most general higher derivative theories of gravity. We also discuss the existence of phase transitions.

“…This deformation is given by the operator [25]: The index notations are detailed in appendix A but here we discuss the general structure of this operator. This operator contains two key components.…”

Section: Introductionmentioning

confidence: 99%

“…For the case when we have a single deformation operator, it was shown in [25][26][27][28] that the supercharge contour can be removed from the twist by stretching it away until it acts on the initial and final states of the process. This allows us to separate out the action of the 'bare twist' σ 2 from the action of the supercharge.…”

Section: Introductionmentioning

confidence: 99%

Full action of two deformation operators in the D1D5 CFT

Carson

Hampton

Mathur

2017

Self Cite

We are interested in thermalization in the D1D5 CFT, since this process is expected to be dual to black hole formation. We expect that the lowest order process where thermalization occurs will be at second order in the perturbation that moves us away from the orbifold point. The operator governing the deformation off of the orbifold point consists of a twist operator combined with a supercharge operator acting on this twist. In a previous paper we computed the action of two twist operators on an arbitrary state of the CFT. In the present work we compute the action of the supercharges on these twist operators, thereby obtaining the full action of two deformation operators on an arbitrary state of the CFT. We show that the full amplitude can be related to the amplitude with just the twists through an action of the supercharge operators on the initial and final states. The essential part of this computation consists of moving the contours from the twist operators to the initial and final states; to do this one must first map the amplitude to a covering space where the twists are removed, and then map back to the original space on which the CFT is defined.