Universal RCFT correlators from the holomorphic bootstrap

Mukhi, Sunil; Muralidhara, Girish

doi:10.1007/jhep02(2018)028

Cited by 18 publications

(46 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The modular differential equation has been used 30 years ago by [20] in an attempts to classify rational conformal field theories (RCFT). It has been revived rather recently in many contexts [4,[21][22][23][24][25][26][27][28][29][30]. The kink at c = 33 2 (F) is the one that has twist gap ∆ t = 3.…”

Section: Summary Of Resultsmentioning

confidence: 99%

Modular constraints on superconformal field theories

Bae

Lee

Song

2019

J. High Energ. Phys.

View full text Add to dashboard Cite

We constrain the spectrum of N = (1, 1) and N = (2, 2) superconformal field theories in two-dimensions by requiring the NS-NS sector partition function to be invariant under the Γ θ congruence subgroup of the full modular group SL(2, Z). We employ semi-definite programming to find constraints on the allowed spectrum of operators with or without U (1) charges. Especially, the upper bounds on the twist gap for the non-current primaries exhibit interesting peaks, kinks, and plateau. We identify a number of candidate rational (S)CFTs realized at the numerical boundaries and find that they are realized as the solutions to modular differential equations associated to Γ θ . Some of the candidate theories have been discussed by Höhn in the context of self-dual extremal vertex operator (super)algebra. We also obtain bounds for the charged operators and study their implications to the weak gravity conjecture in AdS 3 . #1 Throughout this paper, we only consider parity invariant CFTs so that left-moving and rightmoving fermions have the same boundary condition.

show abstract

Section: Summary Of Resultsmentioning

confidence: 99%

Modular constraints on superconformal field theories

Bae

Lee

Song

2019

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…The more detailed and comprehensive results of [16] encountered the fact -well-known in representation theory, and noted previously in [15] -that for exceptional algebras, the tensor product of the fundamental representation with itself does not simply give irreducible symmetric and antisymmetric parts. Instead each of these breaks up further into irreps.…”

Section: Jhep02(2021)158mentioning

confidence: 89%

“…4 Instead, the problem has been tackled using the Wronskian method for correlators of RCFT originally proposed in [7,14] -specifically, the correlator of F 4,1 WZW theory was calculated in [7] and the Knizhnik-Zamolodchikov equation was derived for the fundamental primaries of G 2 and F 4 in [15]. More recently, a master formula was obtained in [16] for the 4-point function of primaries for all members of the MMS series described above. 5 Four-point correlation functions in RCFT are expressed as a sum over the modulussquared of conformal blocks that are holomorphic away from coincident points.…”

Section: Introductionmentioning

confidence: 99%

Universal correlators and novel cosets in 2d RCFT

Mukhi

Poddar

2021

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

The two-character level-1 WZW models corresponding to Lie algebras in the Cvitanović-Deligne series A1, A2, G2, D4, F4, E6, E7 have been argued to form coset pairs with respect to the meromorphic E8,1 CFT. Evidence for this has taken the form of holomorphic bilinear relations between the characters. We propose that suitable 4-point functions of primaries in these models also obey bilinear relations that combine them into current correlators for E8,1, and provide strong evidence that these relations hold in each case. Different cases work out due to special identities involving tensor invariants of the algebra or hypergeometric functions. In particular these results verify previous calculations of correlators for exceptional WZW models, which have rather subtle features. We also find evidence that the intermediate vertex operator algebras A0.5 and E7.5, as well as the three-character A4,1 theory, also appear to satisfy the novel coset relation.

show abstract

“…This problem is also motivated by the fact that in CFT the computation of the null-vectors and the subsequent determination of the ODE is much more complicated than determining the fusions rules. A recent discussion on these issues can be found in [44]. In this respect, a key observation is that the rigidity index ι = 2 (4.2) for CFT equations, such as for instance the BPZ equations of order greater than two [6].…”

Section: Discussionmentioning

confidence: 99%

Rigid Fuchsian Systems in 2-Dimensional Conformal Field Theories

Belavin

Haraoka

Santachiara

2018

Commun. Math. Phys.

View full text Add to dashboard Cite

We investigate Fuchsian equations arising in the context of 2-dimensional conformal field theory (CFT) and we apply the Katz theory of Fucshian rigid systems to solve some of these equations. We show that the Katz theory provides a precise mathematical framework to answer the question whether the fusion rules of degenerate primary fields are enough for determining the differential equations satisfied by their correlation functions. We focus on the case of W 3 Toda CFT: we argue that the differential equations arising for four-point conformal blocks with one nth level semi-degenerate field and a fully-degenerate one in the fundamental sl 3 representation are associated to Fuchsian rigid systems. We show how to apply Katz theory to determine the explicit form of the differential equations, the integral expression of solutions and the monodromy group representation. The theory of twisted homology is also used in the analysis of the integral expression. This approach allows to construct the corresponding fusion matrices and to perform the whole bootstrap program: new explicit factorization of W 3 correlation functions as well shift relations between structure constants are also provided.

show abstract

Universal RCFT correlators from the holomorphic bootstrap

Cited by 18 publications

References 31 publications

Modular constraints on superconformal field theories

Modular constraints on superconformal field theories

Universal correlators and novel cosets in 2d RCFT

Rigid Fuchsian Systems in 2-Dimensional Conformal Field Theories

Contact Info

Product

Resources

About