# Virasoro conformal blocks and thermality from classical background fields

@article{Fitzpatrick2015VirasoroCB, title={Virasoro conformal blocks and thermality from classical background fields}, author={A. Liam Fitzpatrick and Jared Kaplan and Matthew T. Walters}, journal={Journal of High Energy Physics}, year={2015}, volume={2015}, pages={1-32} }

A bstractWe 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…

## 248 Citations

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Abstract
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## References

SHOWING 1-10 OF 74 REFERENCES

### The (2, 0) superconformal bootstrap

- Mathematics
- 2016

In this long overdue second installment, we continue to develop the conformal bootstrap program for
N
=
4
superconformal field theories (SCFTs) in four dimensions via an analysis of the…

### Worldline approach to semi-classical conformal blocks

- Mathematics
- 2015

A bstractWe extend recent results on semi-classical conformal blocks in 2d CFT and their relation to 3D gravity via the AdS/CFT correspondence. We consider four-point functions with two heavy and two…

### Chern-Simons interactions in AdS$_3$ and the current conformal block

- Mathematics
- 2014

We compute the four point function of scalar fields in AdS3 charged under U(1) Chern-Simons fields using the bulk version of the operator state mapping. Then we show how this four point function is…

### Emergent spacetime and holographic CFTs

- Mathematics
- 2012

A bstractWe discuss universal properties of conformal field theories with holographic duals. A central feature of these theories is the existence of a low-lying sector of operators whose correlators…

### The bootstrap program for boundary CFTd

- Mathematics
- 2013

A bstractWe study the constraints of crossing symmetry and unitarity for conformal field theories in the presence of a boundary, with a focus on the Ising model in various dimensions. We show that an…

### Chern-Simons interactions in AdS$_3$ and the current conformal block

- Mathematics
- 2014

We compute the four point function of scalar fields in AdS$_3$ charged under $U(1)$ Chern-Simons fields using the bulk version of the operator state mapping. Then we show how this four point function…

### Universal spectrum of 2d conformal field theory in the large c limit

- Physics
- 2014

A bstractTwo-dimensional conformal field theories exhibit a universal free energy in the high temperature limit T → ∞, and a universal spectrum in the Cardy regime, Δ → ∞. We show that a much…

### Lessons from crossing symmetry at large N

- Physics
- 2014

A bstractWe consider the four-point correlator of the stress tensor multiplet in N=4$$ \mathcal{N}=4 $$ SYM. We construct all solutions consistent with crossing symmetry in the limit of large central…

### Poincaré series, 3D gravity and CFT spectroscopy

- Mathematics, Physics
- 2014

A bstractModular invariance strongly constrains the spectrum of states of two dimensional conformal field theories. By summing over the images of the modular group, we construct candidate CFT…