Virasoro conformal blocks and thermality from classical background fields

By A. Fitzpatrick, Jared Kaplan, Matthew T. Walters. Journal of High Energy Physics, 2015

339 citations recorded by the source corpus.

We show that in 2d CFTs at large central charge, the coupling of the stress tensor to heavy operators can be re-absorbed by placing the CFT in a non-trivial background metric. This leads to a more precise computation of the Virasoro conformal blocks between heavy and light operators, which are shown to be equivalent to global conformal blocks evaluated in the new background. We also generalize to the case where the operators carry U(1) charges. The refined Virasoro blocks can be used as the seed for a new Virasoro block recursion relation expanded in the heavy-light limit. We comment on the implications of our results for the universality of black hole thermality in AdS3, or equivalently, the eigenstate thermalization hypothesis for CFT2 at large central charge.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/08308c8d51c1399cadd9b768ee368938970544ba

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. Eric Perlmutter
2. Per Kraus
3. Thomas Hartman
4. K. Jensen
5. E. Hijano
6. M. Gaberdiel
7. River Snively
8. A. Maloney

In Nuclear and High Energy Physics

1. Eric Perlmutter
2. Thomas Hartman
3. Per Kraus
4. D. Harlow
5. K. Jensen
6. A. Maloney
7. Jordan S. Cotler
8. E. Hijano

Citations in the corpus

• Causality constraints in conformal field theory (2015, methodology): “A similar approach has been applied to entanglement entropy [42, 43] and correlation functions of primary operators [18, 25, 43] using conformal bootstrap methods very similar to those deployed in this paper.”
• A stereoscopic look into the bulk (2016, methodology): “Moreover, by utilizing the tools of [54], we are able to prove the result of [22]: that the semiclassical heavy-light Virasoro block is computed by a geodesic Witten diagram in a conical defect or BTZ geometry.”
• Semiclassical Virasoro blocks from AdS3 gravity (2015, methodology): “These two procedures turn out to agree, as discussed in [20].”
• Bounding the space of holographic CFTs with chaos (2016, result): “Actually, the same result holds even in the “heavy-light limit” of [92], in which hv is held fixed as c becomes large.”
• A theory of reparameterizations for AdS3 gravity (2018, background): “with an eective inverse temperature = jj 2ˇ . Of course the full correlator does not obey the KMS condition, and indeed the 1=ccorrections are not periodic in imaginary time. We refer the reader to [69] for further discussions of the physics of this quasi-periodicity and its relation to the Eigensta”
• A proof of the conformal collider bounds (2016, neutral): “An especially exciting question is the quantum origin of universal features of gravitational interactions, such as causality, (non-)locality and attractiveness [16–18, 32, 76–78].”
• Witten diagrams revisited: the AdS geometry of conformal blocks (2015, methodology): “In [34], we put the geodesic approach to use in constructing the holographic dual of the heavy-light Virasoro blocks of [30], where one geodesic essentially backreacts on AdS to generate a conical defect or black hole geometry.”
• Low-dimensional de Sitter quantum gravity (2019, methodology): “The model arising from Euclidean AdS3 computes Virasoro identity blocks [36, 103–109], and provides another method to calculate Virasoro Wilson lines [110–115].”
• Virasoro conformal blocks in closed form (2015, background): “The expansion of the semiclassical representation, on the other hand, contains corrections to the emergent thermality of heavy microstates at large c [10].”