Excitations in the deformed D1D5 CFT

Abstract

We perform some simple computations for the first order deformation of the D1D5 CFT off its orbifold point. It had been shown earlier that under this deformation the vacuum state changes to a squeezed state (with the further action of a supercharge). We now start with states containing one or two initial quanta and write down the corresponding states obtained under the action of deformation operator. The result is relevant to the evolution of an initial excitation in the CFT dual to the near extremal D1D5 black hole: when a left and a right moving excitation collide in the CFT, the deformation operator spreads their energy over a larger number of quanta, thus evolving the state towards the infrared.

One-loop transition amplitudes in the D1D5 CFT

“…We do not consider these supercharges in the present paper, since their action can be separated from the effect of the twists; we hope to return to an analysis of energy conservation and the complete created state in a later work. We note that the result (1.3) is schematically similar to the first-order deformation studied in [26]. Indeed, we expect this form at all orders for the same reason we expect the exponential form of |χ at all orders: each mode on the cylinder maps to a linear combination of single modes with the same SU(2) indices in the twist-free covering space.…”

“…As detailed in [25,26], the supercharge contours can be removed from the twist by stretching them away until they act on the initial and final states of the process. This The cylinder with twist insertions at w 1 and w 2 .…”

Full action of two deformation operators in the D1D5 CFT

“…One readily notes that this result was schematically identical to the first-order case found in [26]. We expect this form at all orders for the same reason we expect the bogoliubov form of |χ at all orders: each mode on the cylinder maps to a linear combination of single modes with the same SU(2) indices in the twist-free covering space.…”

“…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.…”

Warped AdS3 black holes in higher derivative gravity theories

“…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.…”