Partition function of free conformal higher spin theory

Self Cite

Abstract:In [8] we proposed the linear relations between the Weyl anomaly c 1 , c 2 , c 3 coefficients and the 4 coefficients in the chiral anomaly polynomial for (1,0) superconformal 6d theories. These relations were determined up to one free parameter ξ and its value was then conjectured using some additional assumptions. A different value for ξ was recently suggested in arXiv:1702.03518 using an alternative method. Here we confirm that this latter value is indeed the correct one by providing an additional data point: the Weyl anomaly coefficient c 3 for the higher derivative (1,0) superconformal 6d vector multiplet. This multiplet contains the 4-derivative conformal gauge vector, 3-derivative fermion and 2-derivative scalar. We find the corresponding value of c 3 which is proportional to the coefficient C T in the 2-point function of stress tensor using its relation to the first derivative of the Renyi entropy or the second derivative of the free energy on the product of thermal circle and 5d hyperbolic space. We present some general results of the computation of the Rényi entropy and C T from the partition function on S 1 × H d−1 for higher derivative conformal scalars, spinors and vectors in even dimensions. We also give an independent derivation of the conformal anomaly coefficients of the 6d higher derivative vector multiplet from the Seeley-DeWitt coefficients on an Einstein background.

Section: / ∂ Fermionmentioning

confidence: 90%

Section: Computational Schemementioning

confidence: 99%

“…. turn out to factorize [48] into simple factors so that the corresponding eigenvalues on S 1 q × S d−1 are…”

Section: Computational Schemementioning

confidence: 99%

“…The closely related case of S 1 q × S 3 background was discussed, e.g., in section 2.2 of [48]. Starting with I = − …”

Section: ∂ 2 Gauge Vector In D =mentioning

confidence: 99%

“…The scalar part is absent in d = 4 due to gauge invariance that is then present in (B.1) (cf. section 4.1 and [48]). …”

Section: Jhep06(2017)002mentioning

confidence: 99%

See 3 more Smart Citations

C T for higher derivative conformal fields and anomalies of (1, 0) superconformal 6d theories

Beccaria

Tseytlin

2017

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Mixed-symmetry fields in AdS(5), conformal fields, and AdS/CFT

Metsaev

2015

Mixed-symmetry arbitrary spin massive, massless, and self-dual massive fields in AdS(5) are studied. Light-cone gauge actions for such fields leading to decoupled equations of motion are constructed. Light-cone gauge formulation of mixed-symmetry anomalous conformal currents and shadows in 4d flat space is also developed. AdS/CFT correspondence for normalizable and non-normalizable modes of mixed-symmetry AdS fields and the respective boundary mixed-symmetry anomalous conformal currents and shadows is studied. We demonstrate that the light-cone gauge action for massive mixed-symmetry AdS field evaluated on solution of the Dirichlet problem amounts to the light-cone gauge 2-point vertex of mixed-symmetry anomalous shadow. Also we show that UV divergence of the action for mixed-symmetry massive AdS field with some particular value of mass parameter evaluated on the Dirichlet problem amounts to the action of long mixed-symmetry conformal field, while UV divergence of the action for mixed-symmetry massless AdS field evaluated on the Dirichlet problem amounts to the action of short mixed-symmetry conformal field. We speculate on string theory interpretation of a model which involves short low-spin conformal fields and long higher-spin conformal fields.

Higher spin conformal geometry in three dimensions and prepotentials for higher spin gauge fields

Henneaux

Hörtner

Leonard

2016

We study systematically the conformal geometry of higher spin bosonic gauge fields in three spacetime dimensions. We recall the definition of the Cotton tensor for higher spins and establish a number of its properties that turn out to be key in solving in terms of prepotentials the constraint equations of the Hamiltonian (3 + 1) formulation of four-dimensional higher spin gauge fields. The prepotentials are shown to exhibit higher spin conformal symmetry. Just as for spins 1 and 2, they provide a remarkably simple, manifestly duality invariant formulation of the theory. While the higher spin conformal geometry is developed for arbitrary bosonic spin, we explicitly perform the Hamiltonian analysis and derive the solution of the constraints only in the illustrative case of spin 3. In a separate publication, the Hamiltonian analysis in terms of prepotentials is extended to all bosonic higher spins using the conformal tools of this paper, and the same emergence of higher spin conformal symmetry is confirmed. arXiv:1511.07389v2 [hep-th]