Rényi entropy of a free (2, 0) tensor multiplet and its supersymmetric counterpart

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: Jhep06(2017)002supporting

confidence: 69%

Section: Jhep06(2017)002mentioning

confidence: 99%

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

Beccaria

Tseytlin

2017

“…This quantity was computed on the gauge theory side and for free field theories where an agreement was explicitly demonstrated for the free energies computed for both S 3 q and S 1 q × H 2 [12]. In [17] both the nonsupersymmetric and the supersymmeric Renyi entropies are computed for the abelian M5 brane on S 1 q × H 5 and the generalization of the supersymmetric Renyi entropy to the nonabelian M5 brane was obtained in [18] and more generally to the nonabelian (1,0) SCFT's in [19].…”

Section: Introductionmentioning

confidence: 89%

Abelian M5-brane on S6

Gustavsson

2019

We compute the conformal anomaly of the abelian M5 brane on a conical deformation S 6 q of the round six-sphere. Our results agree with corresponding results on S 1 ×H 5 that were obtained in arXiv:1511.00313. For the free energies we obtain missing Casimir energy contributions, inconsequental for the Renyi entropies, and we obtain the proposed constant shift for the Renyi entropy of the selfdual two-form. arXiv:1904.07799v2 [hep-th]

“…where S(q) U (1) is the abelian Renyi entropy that was computed in [12,13] and H(q) is a cubic polynomial in γ = 1/q whose explicit form was found in [11].…”

Section: Introductionmentioning

confidence: 99%

“…Let us now obtain this result in a different way that we will later generalize to the nonabelian case as well. We use the result for the abelian Renyi entropy [12]…”

mentioning

confidence: 99%

Nonabelian M5-brane on S6q

Bak

Gustavsson

2019

We compute the conformal anomaly of a nonabelian M5 brane on S 1 q ×H 5 in the large N limit by using the gravity dual of a black hole. We also obtain a general formula for this conformal anomaly for any gauge group by combining various results already present in the literature.From the conformal anomaly we extract the Casimir energy on R × S 5 . We find agreement with the proposal in arXiv:1507.08553.