Related papers: The Transition Function of $G_2$ over $S^6$

We study two-dimensional topological gauge theories with gauge group equal to the symmetric group $S_n$ and their string theory duals. The simplest such theory is the topological quantum field theory of principal $S_n$ fiber bundles. Its…

We investigate the nucleon's transverse spin-dependent structure function g_2(x, Q^2) in the framework of the operator product expansion and the renormalization group. We construct the complete set of the twist-3 operators for the flavor…

The SU(2) gauge theory with 8 fundamental fermions is studied using unimproved staggered regularization. A phase transition or a crossover at strong coupling, which can be a bulk transition. By using chiral random matrix model we analyze…

The construction of brane setups for the exceptional series E6,E7,E8 of SU(2) orbifolds remains an ever-haunting conundrum. Motivated by techniques in some works by Muto on non-Abelian SU(3) orbifolds, we here provide an algorithmic…

We establish a structure result for the universal abelian variety over the moduli space A_5, in terms of discriminant curves of conic bundles over a del Pezzo surface. In particular, this gives a very simple unirational parametrization of…

We examine $E_6$ GUT models (both SUSY and non-SUSY) with D-parity violating intermediate trinification symmetry $\left(SU(3)_C\otimes SU(3)_L\otimes SU(3)_R\right)(g_{3L}\neq g_{3R})$ where the D-parity breaking is achieved by quantum…

We discuss the notion of the orbifold transform, and illustrate it on simple examples. The basic properties of the transform are presented, including transitivity and the exponential formula for symmetric products. The connection with the…

We developed a unified framework based on a special (non-regular) embedding of the exceptional group $E_6$ in which the main stage of symmetry breaking chain realizes $E_6\to G(2) \times SU(3)_A$. The exceptional factor $G(2)$ plays the…

We construct a compactification of the universal moduli space of semistable principal $G$-bundles over $\overline{\textrm{M}}_{g}$, the fibers of which over singular curves are the moduli spaces of $\delta$-semistable singular principal…

A principal torus bundle over a complex manifold with even dimensional fiber and characteristic class of type $(1,1)$ admits a family of regular generalized complex structures (GCS) with the fibers as leaves of the associated symplectic…

We construct two parametrizations of the non compact exceptional Lie group G=E7(-25), based on a fibration which has the maximal compact subgroup K=(E6 x U(1))/Z_3 as a fiber. It is well known that G plays an important role in the N=2 d=4…

We study minimal complex surfaces S of general type with q(S)=q and p_g(S)=2q-3, q>= 5. We give a complete classification in case that S has a fibration onto a curve of genus >=2. For these surfaces K^2=8\chi. In general we prove that…

We compare two notions of $G$-fiber bundles and $G$-principal bundles in the literature, with an aim to clarify early results in equivariant bundle theory that are needed in current work of equivariant algebraic topology. We also give…

We give the general presciption for calculating the moduli of irreducible, stable SU(n) holomorphic vector bundles with positive spectral covers over elliptically fibered Calabi-Yau threefolds. Explicit results are presented for Hirzebruch…

Through AGT conjecture, we show how triality observed in \N=2 SU(2) N_f=4 QCD can be interpreted geometrically as the interplay among six of Kummer's twenty-four solutions belonging to one fixed Riemann scheme in the context of…

We consider some infinitesmal and global deformations of G_2 structures on 7-manifolds. We discover a canonical way to deform a G_2 structure by a vector field in which the associated metric gets "twisted" in some way by the vector cross…

We consider a relative Fourier-Mukai transform defined on elliptic fibrations over an arbitrary normal base scheme. This is used to construct relative Atiyah sheaves and generalize Atiyah's and Tu's results about semistable sheaves over…

We study 6d E-string theory with defects on a circle. Our basic strategy is to apply the geometric transition to the supersymmetric gauge theories. First, we calculate the partition functions of the 5d SU(3)$_0$ gauge theory with 10…

Let X be an Abelian surface and C a holomorphic curve in X representing a primitive homology class. The space of genus g curves in the class of C is g dimensional. We count the number of such curves that pass through g generic points and we…

Let $C$ be a hyperelliptic curve of genus $g \geq 3$. We give a new description of the theta map for moduli spaces of rank 2 semistable vector bundles with trivial determinant. In orther to do this, we describe a fibration of (a birational…