相关论文: Kleinian Singularities and the Ground Ring of C=1 …

We review the relationship between discrete groups of symmetries of Euclidean three-space, constructions in algebraic geometry around Kleinian singularities including versions of Hilbert and Quot schemes, and their relationship to…

String theory is a quantum theory that reproduces the results of General Relativity at long distances but is completely different at short distances. Mathematically, string theory is based on a very new -- and little understood -- framework…

We consider a class of integrable quantum field theories in 1+1 dimensions whose classical equations have kink solutions with internal collective coordinates that transform under a non-abelian symmetry group. These generalised sine-Gordon…

We discuss the effect of perturbations on the ground rings of $c=1$ string theory at the various compactification radii defining the $A_N$ points of the moduli space. We argue that perturbations by plus-type moduli define ground varieties…

We study compactifications of the 6d E-string theory, the theory of a small E_8 instanton, to four dimensions. In particular we identify N=1 field theories in four dimensions corresponding to compactifications on arbitrary Riemann surfaces…

This thesis gives a complete description of the Grothendieck group and divisor class group for large families of two and three dimensional singularities. The main results presented throughout, and summarised in Theorem 8.1.1, give an…

String theory, as a theory containing quantum gravity, is usually thought to require more dimensions of spacetime than the usual 3+1. Here I argue on physical grounds that needing extra dimensions for strings may well be an artefact of…

In this paper we propose a unified approach to (topological) string theory on certain singular spaces in their large volume limit. The approach exploits the non-commutative structure of D-branes, so the space is described by an algebraic…

Spacetime singularities are studied in both the $D+d$-dimensional string theory and its $D$-dimensional effective theory, obtained by the Kaluza-Klein compactification. It is found that spacetime singularities in the low dimensional…

We define a notion of stability for chiral ring of four dimensional N=1 theory by introducing test chiral rings and generalized a maximization. We conjecture that a chiral ring is the chiral ring of a superconformal field theory if and only…

The question of whether the holomorphic collinear singularities of graviton amplitudes define a consistent chiral algebra has garnered much recent attention. We analyse a version of this question for infinitesimal perturbations around the…

An interpretation of spacelike singularities in string theory uses target space duality to relate the collapsing Schwarzschild geometry near the singularity to an inflationary cosmology in dual variables. An appealing picture thus results…

We describe the derived category of coherent sheaves on the minimal resolution of the Kleinian singularity associated to a finite subgroup G of SL(2). Then, we give an application to the Euler-characteristic version of the Hall algebra of…

We study string theory in supersymmetric time-dependent backgrounds. In the framework of general relativity, supersymmetry for spacetimes without flux implies the existence of a covariantly constant null vector, and a relatively simple form…

Let $G$ be a finite subgroup of $\text{SL}(2,\Bbbk)$ and let $R = \Bbbk[x,y]^G$ be the coordinate ring of the corresponding Kleinian singularity. In 1998, Crawley-Boevey and Holland defined deformations $\mathcal{O}^\lambda$ of $R$…

Differential properties of Klein-Gordon and electromagnetic fields on the space-time of a straight cosmic string are studied with the help of methods of the differential space theory. It is shown that these fields are smooth in the interior…

Kleinian singularities are quotients of $\mathbb{C}^2$ by finite subgroups of $\mathrm{SL}_2(\mathbb{C})$. They are in bijection with the simply-laced Dynkin diagrams via the McKay correspondence. Anti-Poisson involutions and their fixed…

We investigate Brans-Dicke dilaton gravity theories in 2+1 dimensions. We show that the reduced field equations for solutions with diagonal metric and depending only on one spacetime coordinate have a continuous O(2) symmetry. Using this…

We discuss aspects of global and gauged symmetries in quantum field theory and quantum gravity, focusing on discrete gauge symmetries. An effective Lagrangian description of $\Z_p$ gauge theories shows that they are associated with an…

We study a class of four-dimensional N=1 superconformal field theories obtained from the six-dimensional (1,0) theory, on M5-branes on C^2/Z_k orbifold singularity, compactified on a Riemann surface. This produces various quiver gauge…