Partition Sums and Entropy Bounds in Weakly Coupled CFT

David Kutasov; Finn Larsen

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Partition Sums and Entropy Bounds in Weakly Coupled CFT

David Kutasov, Finn Larsen

High Energy Physics - Theory · Submitted 29 Sep 2000

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Certain modular properties exhibited by the partition functions help to determine the finite volume corrections, which play a role in the discussion of entropy bounds.

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We use the partition functions on S^1 x S^n of various conformal field theories in four and six dimensions in the limit of vanishing coupling to study the high temperature thermodynamics. Certain modular properties exhibited by the partition functions help to determine the finite volume corrections, which play a role in the discussion of entropy bounds.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We use the partition functions on S^1 x S^n of various conformal field theories in four and six dimensions in the limit of vanishing coupling to study the high temperature thermodynamics.	method 0.68	0.93	0.09	asserted 0.98
s1	Certain modular properties exhibited by the partition functions help to determine the finite volume corrections, which play a role in the discussion of entropy bounds.	interpretation 0.30	0.61	0.20	asserted 0.98

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Original abstract

We use the partition functions on S^1 x S^n of various conformal field theories in four and six dimensions in the limit of vanishing coupling to study the high temperature thermodynamics. Certain modular properties exhibited by the partition functions help to determine the finite volume corrections, which play a role in the discussion of entropy bounds.

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References

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Cited by 12 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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Partition function of free conformal higher spin theory
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The canonical partition function of free conformal higher-spin theory is computed in closed form for all even dimensions, and the summed Casimir energy vanishes under the regularization that also cancels the conformal...
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For a conformal field theory on a d-dimensional spatial torus, the high-energy density of states is determined solely by the Casimir energy density on a parallel-plate geometry, generalizing the two-dimensional Cardy formula.
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The regularized product of one-loop partition functions over all free massless higher spins equals one, a cancellation attributed to the theory's large gauge symmetry.
Partition Functions and Casimir Energies in Higher Spin AdS_{d+1}/CFT_d
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The one-loop free energy and Casimir energy of higher-spin gravity in AdS_{d+1} match the order-N^0 terms of large-N singlet-sector free scalar and fermion CFTs on S^1 x S^{d-1} in all dimensions.
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How the literature uses it

25 arXiv papers cite this in 36 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 27 sentences without a confident label

Uses its method or tool 3 papers

Following the procedure outlined above, we rewrite the partition function [ref] of a $d$-dimensional free scalar as [ref] : [equation] where the integral contour $C$ encloses all the simple poles of the integrand.

Modularity in $d > 2$ free conformal field theory · d=2 · 0.90
The brane index calculation will thus require a generalization (in presence of various fugacities) of the operator counting method in [ref] as in our previous applications in [ref] .

Large $N$ Schur index of $\mathcal N=4$ SYM from semiclassical D3 brane · Summary of results · 0.85
Let us note that the same results can be found by first mapping the conformal scalar on $S^1×S^d$ to flat $ℝ^d+1$ space and then applying the operator counting method (see, e.g., [ref] ).To recall, one has $(dlogr)^2+dS_5 = 1/r^2ds^2_ℝ^6$ so that the energies in $S^1×S^5$ may be identified with the scaling dimensions in $ℝ^6$.

Large N expansion of superconformal index of k=1 ABJM theory and semiclassical M5 brane partition function · Single-particle partition functions from operator counting on twisted $ℝ^6$ · 0.93

Cites it as background 5 papers

Checks of the validity of the Cardy-Verlinde formula in the high-temperature limit of free field theories were the subject of several papers [ref] .

Thermodynamics of conformal fields in topologically non-trivial space-time backgrounds · Introduction · 0.86
Consider for example the thermal partition function of a $d$-dimensional conformally coupled free scalar [ref] .

Modularity in $d > 2$ free conformal field theory · Mellin representation of the partition function · 0.98
Let us recall, as an analogy, that absence of $β^n$ ($n≥2$) corrections for in the case of the logarithm of the thermodynamic partition function $Z()̱$ was observed in the past for the standard conformal fields [ref] where this follows from a simple modular transformation property of $Z()̱$.

Superconformal index of higher derivative $\mathcal N=1$ multiplets in four dimensions · Superconformal index and its small $β$ expansion: a review · 0.81

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