Conformal embedding and twisted theta functions at level one

Abstract We identify vertex operator algebras (VOAs) of a class of Argyres-Douglas (AD) matters with two types of non-abelian flavor symmetries. They are the W algebras defined using nilpotent orbit with partition [qm, 1s]. Gauging above AD matters, we can find VOAs for more general $$ \mathcal{N} $$ N = 2 SCFTs engineered from 6d (2, 0) theories. For example, the VOA for general (AN − 1, Ak − 1) theory is found as the coset of a collection of above W algebras. Various new interesting properties of 2d VOAs such as level-rank duality, conformal embedding, collapsing levels, coset constructions for known VOAs can be derived from 4d theory.

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2 Jacobi’s theta functions of one variable and the triple product identity

Theta functions, elliptic functions and π ◽

10.1515/9783110541915-002 ◽

2020 ◽

pp. 15-28

Keyword(s):

Theta Functions ◽

Triple Product ◽

Product Identity

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Second-order integrable Lagrangians and WDVV equations

Letters in Mathematical Physics ◽

10.1007/s11005-021-01403-3 ◽

2021 ◽

Vol 111 (2) ◽

Author(s):

E. V. Ferapontov ◽

M. V. Pavlov ◽

Lingling Xue

Keyword(s):

Lagrangian Density ◽

Theta Functions ◽

Second Order ◽

Elementary Functions ◽

Lagrange Equations ◽

Wdvv Equations ◽

Integrability Conditions ◽

Jacobi Theta Functions

AbstractWe investigate the integrability of Euler–Lagrange equations associated with 2D second-order Lagrangians of the form $$\begin{aligned} \int f(u_{xx},u_{xy},u_{yy})\ \mathrm{d}x\mathrm{d}y. \end{aligned}$$ ∫ f ( u xx , u xy , u yy ) d x d y . By deriving integrability conditions for the Lagrangian density f, examples of integrable Lagrangians expressible via elementary functions, Jacobi theta functions and dilogarithms are constructed. A link of second-order integrable Lagrangians to WDVV equations is established. Generalisations to 3D second-order integrable Lagrangians are also discussed.

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Higher depth mock theta functions and q-hypergeometric series

Forum Mathematicum ◽

10.1515/forum-2021-0013 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Joshua Males ◽

Andreas Mono ◽

Larry Rolen

Keyword(s):

Theta Function ◽

Modular Forms ◽

Hypergeometric Series ◽

Theta Functions ◽

Mock Theta Function ◽

Mock Theta Functions ◽

Maass Forms ◽

Mock Modular Forms ◽

Harmonic Maass Forms

Abstract In the theory of harmonic Maaß forms and mock modular forms, mock theta functions are distinguished examples which arose from q-hypergeometric examples of Ramanujan. Recently, there has been a body of work on higher depth mock modular forms. Here, we introduce distinguished examples of these forms, which we call higher depth mock theta functions, and develop q-hypergeometric expressions for them. We provide three examples of mock theta functions of depth two, each arising by multiplying a classical mock theta function with a certain specialization of a universal mock theta function. In addition, we give their modular completions, and relate each to a q-hypergeometric series.

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On local and integrated stress-tensor commutators

Journal of High Energy Physics ◽

10.1007/jhep07(2021)148 ◽

2021 ◽

Vol 2021 (7) ◽

Author(s):

Mert Besken ◽

Jan de Boer ◽

Grégoire Mathys

Keyword(s):

Stress Tensor ◽

Free Field ◽

Virasoro Algebra ◽

Light Sheet ◽

Operator Product ◽

Local Form ◽

Two Dimensional ◽

Conformal Embedding ◽

General Aspects ◽

The Right

Abstract We discuss some general aspects of commutators of local operators in Lorentzian CFTs, which can be obtained from a suitable analytic continuation of the Euclidean operator product expansion (OPE). Commutators only make sense as distributions, and care has to be taken to extract the right distribution from the OPE. We provide explicit computations in two and four-dimensional CFTs, focusing mainly on commutators of components of the stress-tensor. We rederive several familiar results, such as the canonical commutation relations of free field theory, the local form of the Poincaré algebra, and the Virasoro algebra of two-dimensional CFT. We then consider commutators of light-ray operators built from the stress-tensor. Using simplifying features of the light sheet limit in four-dimensional CFT we provide a direct computation of the BMS algebra formed by a specific set of light-ray operators in theories with no light scalar conformal primaries. In four-dimensional CFT we define a new infinite set of light-ray operators constructed from the stress-tensor, which all have well-defined matrix elements. These are a direct generalization of the two-dimensional Virasoro light-ray operators that are obtained from a conformal embedding of Minkowski space in the Lorentzian cylinder. They obey Hermiticity conditions similar to their two-dimensional analogues, and also share the property that a semi-infinite subset annihilates the vacuum.

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