相关论文: Mock modularity at work, or black holes in a fores…

Using constraints from supersymmetry and string perturbation theory, we determine the string loop corrections to the hypermultiplet moduli space of type II strings compactified on a generic Calabi-Yau threefold. The corresponding…

False theta functions are functions that are closely related to classical theta functions and mock theta functions. In this paper, we study their modular properties at all ranks by forming modular completions analogous to modular…

Modular equations occur in number theory, but it is less known that such equations also occur in the study of deformation properties of quasiconformal mappings. The authors study two important plane quasiconformal distortion functions,…

This review summarizes the recent developments in topological string theory from the author's perspective, mostly focused on aspects of research in which the author is involved. After a brief overview of the theory, we discuss two aspects…

This paper investigates the algebraic structure that exists on perturbative BPS-states in the superstring, compactified on the product of a circle and a Calabi-Yau fourfold. This structure was defined in a recent article by Harvey and…

String theory can accommodate black holes with the black hole parameters related to string moduli. It is a well known but remarkable feature that the near horizon geometry of a large class of black holes arising from string theory contains…

The presence of RR and NS three-form fluxes in type IIB string compactification on a Calabi-Yau orientifold gives rise to a nontrivial superpotential W for the dilaton and complex structure moduli. This superpotential is computable in terms…

The focus of this thesis is on (1) the role of Ka\v c-Moody (KM) algebras in string theory and the development of techniques for systematically building string theory models based on higher level ($K\geq 2$) KM algebras and (2) fractional…

We show that modularity and the gap condition make the holomorphic anomaly equation completely integrable for non-compact Calabi-Yau manifolds. This leads to a very efficient formalism to solve the topological string on these geometries in…

Hypergeometric functions over finite fields were introduced by Greene in the 1980s as a finite field analogue of classical hypergeometric series. These functions, and their generalizations, naturally lend themselves to, and have been widely…

The derivative expnsion in the context of IIB string scattering compactified on non-trivial K3 and other Calabi-Yau manifolds is formulated. The scattering data in terms of automorphic functions can be inverted to find the these metrics.…

By identifying the moduli space of coupling constants in the SYM description of toroidal compactifications of M(atrix)-Theory, we construct the M(atrix) description of the moduli spaces of Type IIA string theory compactified on T^n.…

In this paper, we prove an almost 40 year old conjecture by H. Cohen concerning the generating function of the Hurwitz class number of quadratic forms using the theory of mock modular forms. This conjecture yields an infinite number of so…

We obtain constraints from black hole superradiance in an ensemble of compactifications of type IIB string theory. The constraints require knowing only the axion masses and self-interactions, and are insensitive to the cosmological model.…

It is well known that Ramanujan conjectured congruences modulo powers of $5$, $7$ and and $11$ for the partition function. These were subsequently proved by Watson (1938) and Atkin (1967). In 2009 Choi, Kang, and Lovejoy proved congruences…

Sander Zwegers showed that Ramanujan's mock theta functions are $q$-hypergeometric series, whose $q$-expansion coefficients are half of the Fourier coefficients of a non-holomorphic modular form. George Andrews, Henri Cohen, Freeman Dyson,…

We discuss a set of heterotic and type II string theory compactifications to 1+1 dimensions that are characterized by factorized internal worldsheet CFTs of the form $V_1\otimes \bar V_2$, where $V_1, V_2$ are self-dual (super) vertex…

We continue the program of constructing (pre)modular tensor categories from 3-manifolds first initiated by Cho-Gang-Kim using $M$ theory in physics and then mathematically studied by Cui-Qiu-Wang. An important structure involved is a…

Ramanujan derived a sequence of even weight $2n$ quasimodular forms $U_{2n}(q)$ from derivatives of Jacobi's weight $3/2$ theta function. Using the generating function for this sequence, one can construct sequences of quasimodular forms of…

String compactifications on an orbi-folded torus with complex structure give rise to chiral fermions, spontaneously broken CP, modular invariance. We show that this allows simple effective theories of flavour and CP where: i) the QCD angle…