The large N vector model on S 1 × S 2

Abstract We develop a method to evaluate the partition function and energy density of a massive scalar on a 2-sphere of radius r and at finite temperature β as power series in β r $$ \frac{\beta }{r} $$ . Each term in the power series can be written in terms of polylogarithms. We use this result to...

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Main Authors: Justin R. David, Srijan Kumar
Format: Article
Language:English
Published: SpringerOpen 2025-03-01
Series:Journal of High Energy Physics
Subjects:
Online Access:https://doi.org/10.1007/JHEP03(2025)169
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author Justin R. David
Srijan Kumar
author_facet Justin R. David
Srijan Kumar
author_sort Justin R. David
collection DOAJ
description Abstract We develop a method to evaluate the partition function and energy density of a massive scalar on a 2-sphere of radius r and at finite temperature β as power series in β r $$ \frac{\beta }{r} $$ . Each term in the power series can be written in terms of polylogarithms. We use this result to obtain the gap equation for the large N, critical O(N) model with a quartic interaction on S 1 × S 2 in the large radius expansion. Solving the gap equation perturbatively we obtain the leading finite size corrections to the expectation value of stress tensor for the O(N) vector model on S 1 × S 2. Applying the Euclidean inversion formula on the perturbative expansion of the thermal two point function we obtain the finite size corrections to the expectation value of the higher spin currents of the critical O(N) model. Finally we show that these finite size corrections of higher spin currents tend to that of the free theory at large spin as seen earlier for the model on S 1 × R 2.
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spelling doaj-art-c8e8aeabd9544d79a0e787f49b5e93332025-08-20T03:06:48ZengSpringerOpenJournal of High Energy Physics1029-84792025-03-012025313810.1007/JHEP03(2025)169The large N vector model on S 1 × S 2Justin R. David0Srijan Kumar1Centre for High Energy Physics, Indian Institute of ScienceCentre for High Energy Physics, Indian Institute of ScienceAbstract We develop a method to evaluate the partition function and energy density of a massive scalar on a 2-sphere of radius r and at finite temperature β as power series in β r $$ \frac{\beta }{r} $$ . Each term in the power series can be written in terms of polylogarithms. We use this result to obtain the gap equation for the large N, critical O(N) model with a quartic interaction on S 1 × S 2 in the large radius expansion. Solving the gap equation perturbatively we obtain the leading finite size corrections to the expectation value of stress tensor for the O(N) vector model on S 1 × S 2. Applying the Euclidean inversion formula on the perturbative expansion of the thermal two point function we obtain the finite size corrections to the expectation value of the higher spin currents of the critical O(N) model. Finally we show that these finite size corrections of higher spin currents tend to that of the free theory at large spin as seen earlier for the model on S 1 × R 2.https://doi.org/10.1007/JHEP03(2025)169Thermal Field Theory1/N ExpansionScale and Conformal Symmetries
spellingShingle Justin R. David
Srijan Kumar
The large N vector model on S 1 × S 2
Journal of High Energy Physics
Thermal Field Theory
1/N Expansion
Scale and Conformal Symmetries
title The large N vector model on S 1 × S 2
title_full The large N vector model on S 1 × S 2
title_fullStr The large N vector model on S 1 × S 2
title_full_unstemmed The large N vector model on S 1 × S 2
title_short The large N vector model on S 1 × S 2
title_sort large n vector model on s 1 s 2
topic Thermal Field Theory
1/N Expansion
Scale and Conformal Symmetries
url https://doi.org/10.1007/JHEP03(2025)169
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