## Liouville п¬Ѓeld Modular forms and Elliptic Genera

### Mathieu Moonshine and the Geometry of K3 Surfaces

Lecture Notes on Automorphic Forms and Physics. The Virasoro conjecture proposed by Eguchi-Hori-Xiong and S. Katz predicts that the generating function of Gromov-Witten invariants is annihilated by infinitely many differential operators which form a half branch of the Virasoro algebra. In this paper, we study the genus-1 case of the conjecture, Virasoro group representations fall into the Virasoro coadjoint orbits where each orbit is labelled by at most two quantum numbers (an integer and a continuous parameter) and states in a given orbit are specified by their charges under Virasoro generators L_n's. We show that local (classical) gravity probes can only measure orbit invariant quantities. Details of the Virasoro charges associated.

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Double-Weyl Phonons in Transition-Metal Monosilicides. An elliptic Virasoro symmetry in 6d Fabrizio Nieri Department of Physics and Astronomy, Uppsala University, Box 516, SE-75120 Uppsala, Sweden. E-mail: fb.nieri@gmail.com Abstract: We de ne an elliptic deformation of the Virasoro algebra. We conjecture that the R4 Г—T2 Nekrasov partition function reproduces the chiral blocks of this algebra. We support this proposal by showing that at special, The Virasoro conjecture proposed by Eguchi-Hori-Xiong and S. Katz predicts that the generating function of Gromov-Witten invariants is annihilated by infinitely many differential operators which form a half branch of the Virasoro algebra..

Modular invariance and Virasoro algebra in geometry Kefeng Liu liu@math.ucla.edu Department of Mathematics UCLA Box 951555 Los Angeles, CA 90095-1555 USA Abstract I will discuss certain applications of modular invariance and Vi-rosoro algebra in geometry and topology, through elliptic genera and moduli spaces of Riemann surfaces. Created Date: 3/13/2007 2:04:04 PM Lecture Notes on Automorphic Forms and Physics Miranda C. N. Cheng [;\ [Department of Mathematics, Harvard University, Cambridge, MA 02138, USA \Department of Physics, Harvard University, Cambridge, MA 02138, USA Abstract This is a type-up of the lecture notes for a series of lectures on the topic \Automorphic Forms and Physics", given in the prepara-tory school for the вЂ¦

### CLASSIFYING SPACES VIRASORO EQUIVARIANT BUNDLES ELLIPTIC

q-alg/9705012 PDF arXiv - MAFIADOC.COM. Modular Invariant Virasoro Modules and Elliptic Curves MURRAY R. BREMNER* Department of Mathematics, Yale University, Box 2155 Yale Station, New Haven, CT 06520, U.S.A. (Received: 1 October 1989) Abstract. Given a rational number ~, when does the tensor product of two modular invariant Virasoro modules have central charge (? I show that the resulting equations define elliptic вЂ¦, Physics Research Publications from the Research School of Physics and Engineering.

### Elliptic deformations of quantum Virasoro and Wn algebras

Quantum field theory in curved graphene spacetimes. Adimurthi, ; Yadava, S. L. (1992) Nonexistence of nodal solutions of elliptic equations with critical growth in R 2 Transactions of the American Mathematical Societ, 332 (1). pp. 449-458. ISSN 0002-9947 the Weierstrass elliptic and related functions are used. All the necessary formulae can All the necessary formulae can be found in standard mathematical literature, e.g. [38], or вЂ¦.

CWRU Coffee Voting System Toggle navigation CWRU Coffee Home; Current Votes; My Votes pdf. Quantum field theory in curved graphene spacetimes, Lobachevsky geometry, Weyl symmetry, Hawking effect, and all that. 76 Pages. Quantum field theory in curved graphene spacetimes, Lobachevsky geometry, Weyl symmetry, Hawking effect, and all that. Author. Gaetano Lambiase. Download with Google Download with Facebook or download with email. Quantum field theory in вЂ¦

## [1511.00574] An elliptic Virasoro symmetry in 6d

Free п¬Ѓeld constructions for the elliptic algebra Aqp sl. Analog condensed matter systems present an exciting opportunity to simulate early Universe models in table-top experiments. We consider a recent proposal for an analog condensed matter experiment to simulate the relativistic quantum decay of the false vacuum., q-Virasoro algebra and by Feigin et al[13,21] for q-deformed W algebra, which is some elliptic deforma- tion of aп¬ѓne algebra. The elliptic algebra A q,p;Л†ПЂ (glc.

### Elliptic deformations of quantum Virasoro and Wn algebras

Symmetries in Conformal Field Theory Accueil - IHES. elliptic genus from supergravity. In carrying out the computation we consider п¬Ѓrst, in In carrying out the computation we consider п¬Ѓrst, in section 6, the supergravity contributions, and next, in section 7, the contributions from, The elliptic genus of K3 and CFT International Workshop \Mock Modular Forms and Physics" IMSc, Chennai, India, April 14-18, 2014 Katrin Wendland.

### Modular invariant Virasoro modules and elliptic curves

Tan Zhao Irreducible Virasoro modules from tensor products. the Weierstrass elliptic and related functions are used. All the necessary formulae can All the necessary formulae can be found in standard mathematical literature, e.g. [38], or вЂ¦, Keywords: elliptic algebra, deformed Virasoro symmetry, root of unity limit 1. Introduction Since the proposal of AGT(W) relation [2], 2d/4d correspondence and its generalizations 1, have been intensively studied. Originally, it was the correspondence between the Nekrasov partition function of 4d N = 2 supersymmetric SU(N) gauge theory and the conformal block of 2d CFT with the W N symmetry.

### Research publications RSPE - ANU

www.slac.stanford.edu. Examples of Lie algebras Kac-Moody algebras Elliptic Afп¬Ѓne algebras DJKM algebra Outline - Virasoro algebra - Heisenberg/Weyl algebras - Kac-Moody algebras This monograph deals with two aspects of the theory of elliptic genus: its topological aspect involving elliptic functions, and its representation theoretic aspect involving vertex operator super-algebras. For the second aspect, elliptic genera are shown to have the structure of modules over.

MIRZAKHANIвЂ™S RECURSION RELATIONS, VIRASORO CONSTRAINTS AND THE KDV HIERARCHY MOTOHICO MULASE1 AND BRAD SAFNUK2 Abstract. We вЂ¦ MODULAR FORMS AND TOPOLOGY KEFENG LIU We want to discuss various applications of modular forms in topology. The starting point is elliptic genus and its generalizations.