Related papers: Small Instantons, del Pezzo Surfaces and Type I' t…
We explore contributions to the 4D effective superpotential which arise from Euclidean D3 branes (``instantons'') that intersect space-filling D-branes. These effects can perturb the effective field theory on the space-filling branes by…
We construct 16 new examples of Calabi--Yau threefolds with Picard group of rank 1. Each of these examples is obtained by smoothing the image of a primitive contraction with exceptional divisor being a del Pezzo surface of degree 6, 7 or…
We study the syzygetic structure of projections of del Pezzo surfaces in order to construct singular Calabi-Yau threefolds. By smoothing those threefolds, we obtain new examples of Calabi-Yau threefolds with Picard group of rank 1. We also…
We consider two simple examples of multi-instanton configurations in type II 4d N=1 superstring compactifications. The first one involves O(1) and U(1) D2-instantons embedded in T^6/(Z_2 x Z_2') geometry with SU(4) gauge symmetry coming…
We analyze in detail the case of a marginally stable D-Brane on a collapsed del Pezzo surface in a Calabi-Yau threefold using the derived category of quiver representations and the idea of aligned gradings. We show how the derived category…
We consider novel nonperturbative effects of type I theories compactified on singular ALE spaces obtained by adding NS branes. Such effects include a description of small $E_8$ instantons at singularities.
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…
Field theory with instantons can be partially regularized by adding degrees of freedom at some scale. These extra degrees of freedom lead to the appearence of the new topological defects. These defects which we call freckles have some…
Two dimensional N=(4,4) gauge theories flow to interacting superconformal field theories on their Higgs branch. We examine worldsheet instantons in these theories through the eyes of a D-brane construction. The effective instanton partition…
Instantons in massless theories do not carry over to massive theories due to Derrick's theorem. This theorem can, however, be circumvented, if a constraint that restricts the scale of the instanton is imposed on the theory. Constrained…
We consider an eight-dimensional Einstein-Yang-Mills theory to explore whether Yang-Mills instantons formed in extra dimensions can induce the dynamical instability of our four-dimensional spacetime. We show that the Yang-Mills instantons…
We study automorphism groups of real del Pezzo surfaces, concentrating on finite groups acting minimally on them. As a result, we obtain a vast part of classification of finite subgroups in the real plane Cremona group.
Lagrangian spheres in the symplectic Del Pezzo surfaces arising as blow-ups of the complex projective plane in 4 or fewer points are classified up to Lagrangian isotopy. Unlike the case of the 5-point blow-up, there is no Lagrangian…
A degree one del Pezzo surface is the blowup of P^2 at 8 general points. By the classical Cayley-Bacharach Theorem, there is a unique 9th point whose blowup produces a rational elliptic surface with a section. Via this relationship, we…
We examine the effects of instantons in four dimensional N=1 supersymmetric gauge theory by including D0-branes in type IIA brane constructions. We examine instanton generated superpotentials in supersymmetric QCD and find that they are due…
Working over a perfect field, I classify normal del Pezzo surfaces with base number one that contain a nonrational singularity. They form a huge infinite hierarchy; contractions of ruled surfaces lie on top of it. Descending the hierarchy…
Motivated by homological mirror symmetry, this paper constructs explicit full exceptional collections for the canonical stacks associated with the series of log del Pezzo surfaces constructed by Johnson and Koll\'ar. These surfaces have…
We find normal forms for del Pezzo surfaces of degree $2$ over algebraically closed fields of characteristic $2$. For each normal form, we describe the structure of the group of automorphisms of the surface. In particular, we classify all…
We classify del Pezzo surfaces with Du Val singularities that have infinite automorphism groups, and describe the connected components of their automorphisms groups.
The effects of instantons close to the cut-off is studied in four dimensional SU(2) gauge theory with higher order derivative terms in the action. It is found in the framework of the dilute instanton gas approximation that the convergence…