Results 11 to 20 of about 477,721 (333)

Lattice realizations of unitary minimal modular invariant partition functions [PDF]

, 1995
The conformal spectra of the critical dilute A-D-E lattice models are studied numerically. The results strongly indicate that, in branches 1 and 2, these models provide realizations of the complete A-D-E classification of unitary minimal modular ...
Andrews G E, Cappelli A, D L O'Brien, Friedan D, Kim D, P A Pearce, Pasquier V, Pasquier V, Pearce P A, Roche Ph, Warnaar S O, Warnaar S O, Warnaar S O, Zhou Y-K   +13 more
core   +4 more sources

Modular properties of massive scalar partition functions [PDF]

Journal of High Energy Physics
We compute the exact thermal partition functions of a massive scalar field on flat spacetime backgrounds of the form ℝ d−q × 𝕋 q+1 and show that they possess an SL(q + 1, ℤ) symmetry.
Ankit Aggarwal, Glenn Barnich
doaj   +2 more sources

Three dimensional pure gravity and generalized Hecke operators

Journal of High Energy Physics, 2020
In this paper, we study mathematical functions of relevance to pure gravity in AdS3. Modular covariance places stringent constraints on the space of such functions; modular invariance places even stronger constraints on how they may be combined into ...
M. Ashrafi
doaj   +1 more source

Holomorphic almost modular forms [PDF]

, 2003
Holomorphic almost modular forms are holomorphic functions of the complex upper half plane which can be approximated arbitrarily well (in a suitable sense) by modular forms of congruence subgroups of large index in $\SL(2,\ZZ)$.
Marklof, Jens
core   +2 more sources

Modular Schur Functions [PDF]

Transactions of the American Mathematical Society, 1994
A new family of symmetric functions is considered. These functions are analogous to the classical Schur functions, but depend on an integer modulus p ⩾ 2 p \geqslant 2 , as well as on a partition λ \lambda .
openaire   +1 more source

Proof of a modular relation between 1-, 2- and 3-loop Feynman diagrams on a torus [PDF]

, 2015
The coefficients of the higher-derivative terms in the low energy expansion of genus-one graviton Type II superstring scattering amplitudes are determined by integrating sums of non-holomorphic modular functions over the complex structure modulus of a ...
D'Hoker, Eric, Green, Michael B., Vanhove, Pierre   +2 more
core   +2 more sources

Tetrahedral modular graph functions

Journal of High Energy Physics, 2017
The low-energy expansion of one-loop amplitudes in type II string theory generates a series of world-sheet integrals whose integrands can be represented by world-sheet Feynman diagrams.
Axel Kleinschmidt, Valentin Verschinin
doaj   +1 more source

Poisson equations for elliptic modular graph functions

Physics Letters B, 2021
We obtain Poisson equations satisfied by elliptic modular graph functions with four links. Analysis of these equations leads to a non–trivial algebraic relation between the various graphs.
Anirban Basu
doaj   +1 more source

On the modular invariance of mass eigenstates and CP violation [PDF]

, 2001
We investigate the modular transformation properties of observable (light) fields in heterotic orbifolds, in the light of recent calculations of CP-violating quantities.
Dent, Thomas
core   +2 more sources

Mathieu moonshine and Siegel Modular Forms

Journal of High Energy Physics, 2021
A second-quantized version of Mathieu moonshine leads to product formulae for functions that are potentially genus-two Siegel Modular Forms analogous to the Igusa Cusp Form. The modularity of these functions do not follow in an obvious manner.
Suresh Govindarajan, Sutapa Samanta
doaj   +1 more source