Modular invariance in finite temperature Casimir effect

Alessio, Francesco; Barnich, Glenn

doi:10.1007/jhep10(2020)134

Cited by 6 publications

(13 citation statements)

References 37 publications

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“…From the above equivalence, the partition function for gravitons with Casimir-type boundary conditions may be obtained from that of a massless scalar field on S 1 2d × R 2 . In turn, as shown in [17] and reviewed in appendix A, the same equivalence holds in the electromagnetic case. In the absence of a chemical potential, α = 0, up to a subtlety related to whether the black body result is subtracted or not, the result can thus also be obtained from the literature on the finite temperature electromagnetic Casimir effect [25,26] (see also [27][28][29][30][31][32][33][34][35] and [36][37][38]) for reviews).…”

Section: Partition Functionmentioning

confidence: 53%

“…The next step in section 4 consists in organizing all JHEP02(2021)216 physical degrees of freedom, first in terms of two massless scalar fields with Dirichlet and Neumann boundary conditions, respectively and then in terms of a single scalar field. In order to do so, we follow recent work on the finite temperature electromagnetic Casimir effect and modular invariance in this context [17] to show that this scalar field should satisfy periodic boundary on an interval of double the length of the separation of the plates. This allows us in section 5 to simply infer the exact result for the partition function for gravitons, with a chemical potential for suitably modified spin angular momentum turned on, from the well-studied case of a massless scalar field with linear momentum in the compact direction turned on [2][3][4]18], together with modular properties and consistent high and low temperature expansions.…”

Section: Jhep02(2021)216mentioning

confidence: 99%

“…In this appendix, we re-derive results on the scalar field formulation and modular covariance in the electromagnetic finite temperature Casimir effect [17]. This is done in terms of suitable polarization vectors, so that the construction may be generalized in a straightforward way to the massless spin 2 case.…”

Section: A Photons In a Casimir Box Revisitedmentioning

confidence: 99%

“…In order to streamline the computation of the partition function and to discuss modular properties, it is useful to go one step further and introduce a formulation with a single scalar field on z ∈ [−d, d] with periodic boundary conditions [17].…”

Section: Jhep02(2021)216mentioning

confidence: 99%

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Gravitons in a Casimir box

Alessio

Barnich

Bronte

2021

J. High Energ. Phys.

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The partition function of gravitons with Casimir-type boundary conditions is worked out. The simplest box that allows one to achieve full analytical control consists of a slab geometry with two infinite parallel planes separated by a distance d. In this setting, linearized gravity, like electromagnetism, is equivalent to two free massless scalar fields, one with Dirichlet and one with Neumann boundary conditions, which in turn may be combined into a single massless scalar with periodic boundary conditions on an interval of length 2d. When turning on a chemical potential for suitably adapted spin angular momentum, the partition function is modular covariant and expressed in terms of an Eisenstein series. It coincides with that for photons. At high temperature, the result provides in closed form all sub-leading finite-size corrections to the standard (gravitational) black body result. More interesting is the low-temperature/small distance expansion where the leading contribution to the partition function is linear in inverse temperature and given in terms of the Casimir energy of the system, whereas the leading contribution to the entropy is proportional to the area and originates from gravitons propagating parallel to the plates.

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Section: Partition Functionmentioning

confidence: 53%

Section: Jhep02(2021)216mentioning

confidence: 99%

Section: A Photons In a Casimir Box Revisitedmentioning

confidence: 99%

Section: Jhep02(2021)216mentioning

confidence: 99%

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Gravitons in a Casimir box

Alessio

Barnich

Bronte

2021

J. High Energ. Phys.

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“…[23] for an early review) may be combined into a single massless scalar field with periodic boundary conditions on an interval of length 2a. Modular covariance for electromagnetism then follows from the scalar field result when understanding what electromagnetic operator corresponds to scalar field momentum in the compact dimension [24]. Moreover, this analysis may be generalized directly to the case of gravitons [25].…”

Section: Jhep12(2021)211mentioning

confidence: 99%

Notes on massless scalar field partition functions, modular invariance and Eisenstein series

Alessio

Barnich

Bonte

2021

J. High Energ. Phys.

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The partition function of a massless scalar field on a Euclidean spacetime manifold ℝd−1 × 𝕋2 and with momentum operator in the compact spatial dimension coupled through a purely imaginary chemical potential is computed. It is modular covariant and admits a simple expression in terms of a real analytic SL(2, ℤ) Eisenstein series with s = (d + 1)/2. Different techniques for computing the partition function illustrate complementary aspects of the Eisenstein series: the functional approach gives its series representation, the operator approach yields its Fourier series, while the proper time/heat kernel/world-line approach shows that it is the Mellin transform of a Riemann theta function. High/low temperature duality is generalized to the case of a non-vanishing chemical potential. By clarifying the dependence of the partition function on the geometry of the torus, we discuss how modular covariance is a consequence of full SL(2, ℤ) invariance. When the spacetime manifold is ℝp × 𝕋q+1, the partition function is given in terms of a SL(q + 1, ℤ) Eisenstein series again with s = (d + 1)/2. In this case, we obtain the high/low temperature duality through a suitably adapted dual parametrization of the lattice defining the torus. On 𝕋d+1, the computation is more subtle. An additional divergence leads to an harmonic anomaly.

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Exact lattice chiral symmetry in 2D gauge theory

Berkowitz,

Cherman,

Jacobson

2024

Phys. Rev. D

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We construct symmetry-preserving lattice regularizations of 2D QED with one and two flavors of Dirac fermions, as well as the “3450” chiral gauge theory, by leveraging bosonization and recently proposed modifications of Villain-type lattice actions. The internal global symmetries act just as locally on the lattice as they do in the continuum, the anomalies are reproduced at finite lattice spacing, and in each case we find a sign-problem-free dual formulation. Published by the American Physical Society 2024

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Modular invariance in finite temperature Casimir effect

Cited by 6 publications

References 37 publications

Gravitons in a Casimir box

Gravitons in a Casimir box

Notes on massless scalar field partition functions, modular invariance and Eisenstein series

Exact lattice chiral symmetry in 2D gauge theory

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