Broken (super) conformal Ward identities at finite temperature

Enrico Marchetto (Mathematical Institute, University of Oxford, Andrew Wiles Building, Woodstock Road, Oxford, OX2 6GG, U.K.) ; Alessio Miscioscia (Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, Hamburg, 22607, Germany) ; Elli Pomoni (Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, Hamburg, 22607, Germany)

When a (super) conformal field theory is placed on a non-trivial manifold, the (super) conformal symmetry is broken. However, it is still possible to derive broken Ward identities for these broken symmetries, which provide additional constraints on the theory. We derive and apply the broken Ward identities associated with the (super) conformal group on the thermal manifold M β = S β 1 × d 1 $$ {\mathcal{M}}_{\beta }={S}_{\beta}^1\times {\mathbb{R}}^{d-1} $$ and M = T 2 × d 2 $$ \mathcal{M}={T}^2\times {\mathbb{R}}^{d-2} $$ . The novel constraints not only systematically reproduce known results, including an implicit formulation of the generalized Cardy formula, but also elegantly relate the thermal energy spectrum with the conformal spectrum.

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      "surname": "Pomoni", 
      "email": "elli.pomoni@desy.de", 
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      "title": "Broken (super) conformal Ward identities at finite temperature"
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      "source": "Springer", 
      "value": "When a (super) conformal field theory is placed on a non-trivial manifold, the (super) conformal symmetry is broken. However, it is still possible to derive broken Ward identities for these broken symmetries, which provide additional constraints on the theory. We derive and apply the broken Ward identities associated with the (super) conformal group on the thermal manifold   <math> <msub> <mi>M</mi> <mi>\u03b2</mi> </msub> <mo>=</mo> <msubsup> <mi>S</mi> <mi>\u03b2</mi> <mn>1</mn> </msubsup> <mo>\u00d7</mo> <msup> <mi>\u211d</mi> <mrow> <mi>d</mi> <mo>\u2212</mo> <mn>1</mn> </mrow> </msup> </math>  $$ {\\mathcal{M}}_{\\beta }={S}_{\\beta}^1\\times {\\mathbb{R}}^{d-1} $$  and   <math> <mi>M</mi> <mo>=</mo> <msup> <mi>T</mi> <mn>2</mn> </msup> <mo>\u00d7</mo> <msup> <mi>\u211d</mi> <mrow> <mi>d</mi> <mo>\u2212</mo> <mn>2</mn> </mrow> </msup> </math>  $$ \\mathcal{M}={T}^2\\times {\\mathbb{R}}^{d-2} $$ . The novel constraints not only systematically reproduce known results, including an implicit formulation of the generalized Cardy formula, but also elegantly relate the thermal energy spectrum with the conformal spectrum."
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Published on:
27 December 2023
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2023 (2023)
Issue 12
Pages 1-48
DOI:
https://doi.org/10.1007/JHEP12(2023)186
arXiv:
2306.12417
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: