Superconformal blocks from Wilson lines with loop corrections

Hikida, Yasuaki; Uetoko, Takahiro

doi:10.1007/jhep08(2018)101

Cited by 20 publications

(30 citation statements)

References 59 publications

(159 reference statements)

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“…We then compared the results with the spectrum of the coset (1.1) and the mass of conical defect geometry of the higher spin gravity constructed in [16]. In particular, the conformal weights in (3.56) give the information of quantum corrections to the masses of conical defects, and it is an important problem to reproduce them from the gravity theory, see [54,55,56]. It is also desired to have more systematic understanding of degenerate representations including generic M and n.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Rectangular W algebras and superalgebras and their representations

Creutzig

Hikida

2019

Phys. Rev. D

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We study W-algebras obtained by quantum Hamiltonian reduction of sl(M n) associated to the sl(2) embedding of rectangular type. The algebra can be realized as the asymptotic symmetry of higher spin gravity with M × M matrix valued fields. In our previous work, we examined the basic properties of the W-algebra and claimed that the algebra can be realized as the symmetry of Grassmannianlike coset even with finite central charge based on a proposal of holography. In this paper, we extend the analysis in the following ways. Firstly, we compute the operator product expansions among low spin generators removing the restriction of n = 2. Secondly, we investigate the degenerate representations in several ways, and see the relations to the coset spectrum and the conical defect geometry of the higher spin gravity. For these analyses, we mainly set M = n = 2. Finally, we extend the previous analysis by introducing N = 2 supersymmetry. *

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Section: Conclusion and Discussionmentioning

confidence: 99%

Rectangular W algebras and superalgebras and their representations

Creutzig

Hikida

2019

Phys. Rev. D

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“…The c-dependence of the contribution of P is given by c p . For the calculation of the matrix elements of the Wilson line operator to order 1/c 3 , to be given in the next section, we shall need the correlators for n = 2, 3 given in (5.9), as well as those for n = 4 with one and two cycles, for n = 5 with two cycles, and for n = 6 with three cycles, given as follows, , T (y 1 ) · · · T (y 5 ) = T 5 [12][345] + 9 more partitions + O(c), T (y 1 ) · · · T (y 6 ) = T X(y) was defined in (5.4) and the states |j, m stand for the tensor product of the free field theory ground state and the spin j representation state of SL(2, R) of weight m. The multiplicative renormalization factor N (ε) is required on general grounds for an exponential operator, while the factor α(ε) renormalizes the coupling to the stress tensor. It will be shown below that the parameters N (ε) and α(ε) may be chosen, order by order in powers of 1/c, so as to cancel the poles in ε, and to define a renormalized matrix element whose scaling dimension is h(j, c),…”

Section: Dimensional Regularizationmentioning

confidence: 99%

“…To order 1/c 2 , the coefficientW 1234 receives contributions from the partitions [12][34], [13] [24] and [14][23], whose denominator functions are given by,…”

Section: Calculation Of the Coefficientsw 12 W 123 Andw 1234mentioning

confidence: 99%

“…where the right column lists a convenient choice of variable to be eliminated with the help of the δ-function. Since N 4 is polynomial in α 1 , α 2 , α 3 , the integrals required to evaluate W [12][34] , W [13] [24] and W [14][23] are of the Euler beta function type of (E.1). They may be readily evaluated and produce the results on the third line of (5.25).…”

Section: C2 Calculation Of W 1234mentioning

confidence: 99%

“…More recently, Wilson lines arose in the context of the AdS 3 /CFT 2 correspondence, first as a tool for computing entanglement entropy in higher spin theories [3,4], and then in the more general context of computing conformal blocks [5,6]. Quantum aspects of these Wilson lines have been studied in [7,8,9,10,11,12]. The related representation of CFT conformal blocks and OPE structures in terms of AdS appeared in [13] and in [14].…”

Section: Introductionmentioning

confidence: 99%

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Renormalization of gravitational Wilson lines

Beşken¹,

D’Hoker²,

Hegde³

et al. 2019

J. High Energ. Phys.

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We continue the study of the Wilson line representation of conformal blocks in twodimensional conformal field theory; these have an alternative interpretation as gravitational Wilson lines in the context of the AdS 3 /CFT 2 correspondence. The gravitational Wilson line involves a path-ordered exponential of the stress tensor, and its expectation value can be computed perturbatively in an expansion in inverse powers of the central charge c. The short-distance singularities which occur in the associated stress tensor correlators require systematic regularization and renormalization prescriptions, whose consistency with conformal Ward identities presents a subtle problem. The regularization used here combines dimensional regularization and analytic continuation. Representation theoretic arguments, based on SL(2, R) current algebra, predict an exact result for the Wilson line anomalous dimension and, by building on previous work, we verify that the perturbative calculations using our regularization and renormalization prescriptions reproduce the exact result to order 1/c 3 included. We also discuss a related, but somewhat simpler, Wilson line in Wess-Zumino-Witten models that yields current algebra conformal blocks, and we emphasize the distinction between Wilson lines constructed out of non-holomorphic and purely holomorphic currents.

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Light cone bootstrap in general 2D CFTs and entanglement from light cone singularity

Kusuki

2019

J. High Energ. Phys.

120

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The light cone OPE limit provides a significant amount of information regarding the conformal field theory (CFT), like the high-low temperature limit of the partition function. We started with the light cone bootstrap in the general CFT 2 with c > 1. For this purpose, we needed an explicit asymptotic form of the Virasoro conformal blocks in the limit z → 1, which was unknown until now. In this study, we computed it in general by studying the pole structure of the fusion matrix (or the crossing kernel). Applying this result to the light cone bootstrap, we obtained the universal total twist (or equivalently, the universal binding energy) of two particles at a large angular momentum. In particular, we found that the total twist is saturated by the value c−1 12 if the total Liouville momentum exceeds beyond the BTZ threshold. This might be interpreted as a black hole formation in AdS 3 .As another application of our light cone singularity, we studied the dynamics of entanglement after a global quench and found a Renyi phase transition as the replica number was varied. We also investigated the dynamics of the 2nd Renyi entropy after a local quench.We also provide a universal form of the Regge limit of the Virasoro conformal blocks from the analysis of the light cone singularity. This Regge limit is related to the general n-th Renyi entropy after a local quench and out of time ordered correlators. the OPE associativity.

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Superconformal blocks from Wilson lines with loop corrections

Cited by 20 publications

References 59 publications

Rectangular W algebras and superalgebras and their representations

Rectangular W algebras and superalgebras and their representations

Renormalization of gravitational Wilson lines

Light cone bootstrap in general 2D CFTs and entanglement from light cone singularity

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