The four-dimensional position operator in theories with broken conformal symmetry

Abstract We demonstrate the simplicity of AdS5× S5 IIB supergravity at one loop level, by studying non-planar holographic four-point correlators in Mellin space. We develop a systematic algorithm for constructing one-loop Mellin amplitudes from the tree-level data, and obtain a simple closed form answer for the $$ \left\langle {\mathcal{O}}_2^{SG}{\mathcal{O}}_2^{SG}{\mathcal{O}}_p^{SG}{\mathcal{O}}_p^{SG}\right\rangle $$ O 2 SG O 2 SG O p SG O p SG correlators. The structure of this expression is remarkably simple, containing only simultaneous poles in the Mellin variables. We also study the flat space limit of the Mellin amplitudes, which reproduces precisely the IIB supergravity one-loop amplitude in ten dimensions. Our results provide nontrivial evidence for the persistence of the hidden conformal symmetry at one loop.

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Resolving modular flow: a toolkit for free fermions

Journal of High Energy Physics ◽

10.1007/jhep12(2020)126 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Johanna Erdmenger ◽

Pascal Fries ◽

Ignacio A. Reyes ◽

Christian P. Simon

Keyword(s):

Complex Analysis ◽

Conformal Symmetry ◽

Standard Technique ◽

Analytic Structure ◽

Point Function ◽

Free Fermions ◽

Modular Evolution ◽

Non Local ◽

Kms Condition ◽

New Formula

Abstract Modular flow is a symmetry of the algebra of observables associated to space-time regions. Being closely related to entanglement, it has played a key role in recent connections between information theory, QFT and gravity. However, little is known about its action beyond highly symmetric cases. The key idea of this work is to introduce a new formula for modular flows for free chiral fermions in 1 + 1 dimensions, working directly from the resolvent, a standard technique in complex analysis. We present novel results — not fixed by conformal symmetry — for disjoint regions on the plane, cylinder and torus. Depending on temperature and boundary conditions, these display different behaviour ranging from purely local to non-local in relation to the mixing of operators at spacelike separation. We find the modular two-point function, whose analytic structure is in precise agreement with the KMS condition that governs modular evolution. Our ready-to-use formulae may provide new ingredients to explore the connection between spacetime and entanglement.

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Notes on gravity multiplet correlators in AdS3 × S3

Journal of High Energy Physics ◽

10.1007/jhep07(2021)125 ◽

2021 ◽

Vol 2021 (7) ◽

Author(s):

Congkao Wen ◽

Shun-Qing Zhang

Keyword(s):

Recursion Relation ◽

Conformal Symmetry ◽

Flat Space ◽

The Other ◽

Tree Level ◽

Space Limit ◽

Compact Expression ◽

Tensor Multiplet ◽

R Symmetry

Abstract We present a compact formula in Mellin space for the four-point tree-level holographic correlators of chiral primary operators of arbitrary conformal weights in (2, 0) supergravity on AdS3× S3, with two operators in tensor multiplet and the other two in gravity multiplet. This is achieved by solving the recursion relation arising from a hidden six-dimensional conformal symmetry. We note the compact expression is obtained after carefully analysing the analytic structures of the correlators. Various limits of the correlators are studied, including the maximally R-symmetry violating limit and flat-space limit.

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