Partition functions of higher derivative conformal fields on conformally related spaces

Mukherjee, Jyotirmoy

doi:10.1007/jhep10(2021)236

Cited by 9 publications

(3 citation statements)

References 44 publications

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“…(A.11) in [4], and also eq. ( 5.25) in [10]. Besides, the massive and the partially massless gravitons combine to form, on the six-sphere, a maximal depth t = s = 2 CHS with residual scalar gauge invariance as discussed in eq.…”

Section: But Acting On Unconstrained Vectorsmentioning

confidence: 97%

GJMS-like operators on symmetric 2-tensors and their gravitational duals

Aros

Bugini

Díaz

2023

J. High Energ. Phys.

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We study a family of higher-derivative conformal operators $$ {P}_{2k}^{(2)} $$ P 2 k 2 acting on transverse-traceless symmetric 2-tensors on generic Einstein spaces. They are a natural generalization of the well-known construction for scalars.We first provide the alternative description in terms of a bulk Poincaré-Einstein metric by making use of the AdS/CFT dictionary and argue that their holographic dual generically consists of bulk massive gravitons. At one-loop quantum level we put forward a holographic formula for the functional determinant of the higher-derivative conformal operators $$ {P}_{2k}^{(2)} $$ P 2 k 2 in terms of the functional determinant for massive gravitons with standard and alternate boundary conditions. The analogous construction for vectors $$ {P}_{2k}^{(1)} $$ P 2 k 1 is worked out as well and we also rewrite the holographic formula for unconstrained vector and traceless symmetric 2-tensor by decoupling the longitudinal part.Finally, we show that the holographic formula provides the necessary building blocks to address the massless and partially massless bulk gravitons. This is confirmed in four and six dimensions, verifying full agreement with results available in the literature.

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Section: But Acting On Unconstrained Vectorsmentioning

confidence: 97%

GJMS-like operators on symmetric 2-tensors and their gravitational duals

Aros

Bugini

Díaz

2023

J. High Energ. Phys.

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“…A similar idea relates the character of conformal fields on the hyperbolic cylinder to characters on the sphere [65,66]. The relation between partition functions in black hole backgrounds and quasinormal modes is in fact quite general [67].…”

Section: Jhep03(2022)165mentioning

confidence: 99%

Characters, quasinormal modes, and Schwinger pairs in dS2 with flux

Grewal

Parmentier

2022

J. High Energ. Phys.

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An integral representation of the 1-loop partition function for charged scalars and spinors, minimally coupled to a uniform U(1) field on S2, is given in terms of SO(1, 2) Harish-Chandra group characters and evaluated exactly in terms of Hurwitz ζ-functions. Analytically continuing the U(1) field, we interpret the path integrals as quasicanonical partition functions in dS2 with an electric field. The character itself is obtained as a trace over states living at the future boundary of de Sitter and has a quasinormal mode expansion. The imaginary part of the partition function captures Schwinger pair creation in the static patch at finite temperature. The thermal enhancement is most noticeable for scalar masses below Hubble and leads to non-monotonicity of the current as a function of the field. This parameter range, when dimensionally reducing from a charged or rotating Nariai spacetime, is excluded by Swampland-inspired bounds. Around the AdS2 black hole, in contrast to dS2, there is a threshold to pair creation.

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“…In fact, this determinant combined with the previous quotient produce the partition function for the 4-derivative conformal gauge vector which is the s = 1 member of the Conformal Higher Spin (CHS) family in 6D (see eqn.A.11 in[4], and also eqn.5.25 in[10]. Besides, the massive and the partially massless gravitons combine to form, on the six-sphere, a maximal depth t = s = 2 CHS with residual scalar gauge invariance as discussed in eqn.3.26 of[11] 3.…”

mentioning

confidence: 91%