Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userNon-Critical Strings, Del Pezzo Singularities And Seiberg-Witten Curves
78
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We study limits of four-dimensional type II Calabi-Yau compactifications with vanishing four-cycle singularities, which are dual to $IT^2$ compactifications of the six-dimensional non-critical string with $E_8$ symmetry. We define proper subsectors of the full string theory, which can be consistently decoupled. In this way we obtain rigid effective theories that have an intrinsically stringy BPS spectrum. Geometrically the moduli spaces correspond to special geometry of certain non-compact Calabi-Yau spaces of an intriguing form. An equivalent description can be given in terms of Seiberg-Witten curves, given by the elliptic simple singularities together with a peculiar choice of meromorphic differentials. We speculate that the moduli spaces describe non-perturbative non-critical string theories.
rate research
Read More
We consider N=2 supersymmetric gauge theories perturbed by tree level superpotential terms near isolated singular points in the Coulomb moduli space. We identify the Seiberg-Witten curve at these points with polynomial equations used to construct what Grothendieck called dessins denfants or childrens drawings on the Riemann sphere. From a mathematical point of view, the dessins are important because the absolute Galois group Gal(bar{Q}/Q) acts faithfully on them. We argue that the relation between the dessins and Seiberg-Witten theory is useful because gauge theory criteria used to distinguish branches of N=1 vacua can lead to mathematical invariants that help to distinguish dessins belonging to different Galois orbits. For instance, we show that the confinement index defined in hep-th/0301006 is a Galois invariant. We further make some conjectures on the relation between Grothendiecks programme of classifying dessins into Galois orbits and the physics problem of classifying phases of N=1 gauge theories.
We show how to map Grothendiecks dessins denfants to algebraic curves as Seiberg-Witten curves, then use the mirror map and the AGT map to obtain the corresponding 4d $mathcal{N}=2$ supersymmetric instanton partition functions and 2d Virasoro conformal blocks. We explicitly demonstrate the 6 trivalent dessins with 4 punctures on the sphere. We find that the parametrizations obtained from a dessin should be related by certain duality for gauge theories. Then we will discuss that some dessins could correspond to conformal blocks satisfying certain rules in different minimal models.
We derive Seiberg-Witten like equations encoding the dynamics of N=2 ADE quiver gauge theories in presence of a non-trivial Omega-background along a two dimensional plane. The epsilon-deformed prepotential and the chiral correlators of the gauge theory are extracted from difference equations that can be thought as a non-commutative (or quantum) version of the Seiberg-Witten curves for the quiver.
We study the dynamics of a N=2 supersymmetric SU(N) gauge theory with fundamental or adjoint matter in presence of a non trivial Omega-background along a two dimensional plane. The prepotential and chiral correlators of the gauge theory can be obtained, via a saddle point analysis, from an equation which can be viewed as a non commutative version of the standard Seiberg and Witten curve.
We derive a family of matrix models which encode solutions to the Seiberg-Witten theory in 4 and 5 dimensions. Partition functions of these matrix models are equal to the corresponding Nekrasov partition functions, and their spectral curves are the Seiberg-Witten curves of the corresponding theories. In consequence of the geometric engineering, the 5-dimensional case provides a novel matrix model formulation of the topological string theory on a wide class of non-compact toric Calabi-Yau manifolds. This approach also unifies and generalizes other matrix models, such as the Eguchi-Yang matrix model, matrix models for bundles over $P^1$, and Chern-Simons matrix models for lens spaces, which arise as various limits of our general result.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
