Related papers: Examples of M5-Brane Elliptic Genera
The open supermembrane contribution to the non-perturbative superpotential of bulk space five-branes in heterotic M-theory is presented. We explicitly compute the superpotential for the modulus associated with the separation of a bulk…
We study modularity properties of generating series of logarithmic Gromov-Witten invariants of elliptic fibrations relative to singular fibers. Motivated by predictions from Vafa-Witten theory, we conjecture that such generating series are…
We describe a duality relation between configurations of M5-branes in M-theory and type IIB theory on Taub-NUT geometries with NSNS and RR 3-form field strength fluxes. The flux parameters are controlled by the angles between the M5-brane…
The kappa--invariant worldvolume action for the NS5--brane in a D=10 type IIA supergravity background is obtained by carrying out the dimensional reduction of the M5--brane action.
We show how, in heterotic M-theory, an M5-brane in the 11-dimensional bulk may end on an ``M9-brane'' boundary, the M5-brane boundary being a Yang monopole 4-brane. This possibility suggests various novel 5-brane configurations of heterotic…
Using reduced Gromov-Witten theory, we define new invariants which capture the enumerative geometry of curves on holomorphic symplectic 4-folds. The invariants are analogous to the BPS counts of Gopakumar and Vafa for Calabi-Yau 3-folds,…
The Gopakumar-Vafa conjecture predicts that the Gromov-Witten invariants of a Calabi-Yau 3-fold can be canonically expressed in terms of integer invariants called BPS numbers. Using the methods of symplectic Gromov-Witten theory, we prove…
Let F be the cyclotomic field of fifth roots of unity. We computationally investigate modularity of elliptic curves over F.
We discuss two simple but useful observations that allow the construction of modular forms from given ones using invariant theory. The first one deals with elliptic modular forms and their derivatives, and generalizes the Rankin-Cohen…
We derive the fivebrane instanton corrections to the hypermultiplet moduli space $M_H$ of Calabi-Yau string vacua using S-duality symmetry of the type IIB formulation. The result is given in terms of a set of holomorphic functions on the…
We study BPS states which arise in compactifications of M-theory on Calabi-Yau manifolds. In particular, we are interested in the spectrum of the particles obtained by wrapping M2-brane on a two-cycle in the CY manifold X. We compute the…
This is the second part of our ongoing project on the relations between Gopakumar-Vafa BPS invariants (GV) and quantum K-theory (QK) on the Calabi--Yau threefolds (CY3). We show that on CY3 a genus zero quantum K-invariant can be written as…
We investigate quantum corrections to the hypermultiplet moduli space M in Calabi-Yau compactifications of type II string theories, with particular emphasis on instanton effects from Euclidean NS5-branes. Based on the consistency of D- and…
By blowing up the ambient space along the curve wrapped by B-branes, we study the brane superpotentials and Ooguri-Vafa invariants on complete intersections Calabi-Yau threefolds. On the topological B-model side, B-brane superpotentials are…
A supersymmetric non-Abelian self-dual gauge theory with the explicit introduction of Kaluza-Klein modes is proposed to give a classical description of multiple M5-branes on $R^5 \times S^1$. The gauge symmetry is parametrized by…
In this paper, we present an investigation of the Gopakumar-Vafa (GV) invariant, a curve-counting integral invariant associated with Calabi-Yau threefolds, as proposed by physicists. Building upon the conjectural definition of the GV…
We present an ansatz for black 2-branes in five dimensional N=2 supergravity theory that carry magnetic charge with respect to general hypermultiplet scalars. We find explicit solutions in certain special cases and examine the constraints…
Recent advances in 11 dimensional Horava-Witten M-theory based on non-standard embeddings with torus fibered Calabi-Yau manifolds have allowed the construction of three generation models with Wilson line breaking to the Standard Model gauge…
We study modular differential equations for the basic weak Jacobi forms in one abelian variable with applications to the elliptic genus of Calabi--Yau varieties. We show that the elliptic genus of any $CY_3$ satisfies a differential…
We show that the stringy K\"ahler moduli space of a generic genus one curve of degree $N$, for $N\le 5$, is the $\Gamma_1(N)$ modular curve $X_1(N)$. This implies a correspondence between the cusps of the modular curves and certain large…