Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userFlavor symmetries and the topology of special Kahler structures at rank 1
58
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We propose a method for determining the flavor charge lattice of the continuous flavor symmetry of rank-1 4d N = 2 superconformal field theories (SCFTs) and IR free gauge theories from topological invariants of the special Kahler structure of the mass-deformed Coulomb branches (CBs) of the theories. The method is based on the middle homology of the total space of the elliptic fibration over the CB, and is a generalization of the F-theory string web description of flavor charge lattices. The resulting lattices, which we call string web lattices, contain not only information about the flavor symmetry of the SCFT but also additional information encoded in the lattice metric derived from the middle homology intersection form. This additional information clearly reflects the low energy electric and magnetic charges of BPS states on the CB, but there are other properties of the string web lattice metric which we have not been able to understand in terms of properties of the BPS spectrum. We compute the string web lattices of all rank-1 SCFTs and IR free gauge theories. We find agreement with results obtained by other methods, and find in a few cases that the string web lattice gives additional information on the flavor symmetry.
rate research
Read More
The scalars in vector multiplets of N=2 supersymmetric theories in 4 dimensions exhibit `special Kaehler geometry, related to duality symmetries, due to their coupling to the vectors. In the literature there is some confusion on the definition of special geometry. We show equivalences of some definitions and give examples which show that earlier definitions are not equivalent, and are not sufficient to restrict the Kaehler metric to one that occurs in N=2 supersymmetry. We treat the rigid as well as the local supersymmetry case. The connection is made to moduli spaces of Riemann surfaces and Calabi-Yau 3-folds. The conditions for the existence of a prepotential translate to a condition on the choice of canonical basis of cycles.
We study the stratification of the singular locus of four dimensional $mathcal{N}=2$ Coulomb branches. We present a set of self-consistency conditions on this stratification which can be used to extend the classification of scale-invariant rank 1 Coulomb branch geometries to two complex dimensions, and beyond. The calculational simplicity of the arguments presented here stems from the fact that the main ingredients needed -- the rank 1 deformation patterns and the pattern of inclusions of rank 2 strata -- are discrete topological data which satisfy strong self-consistency conditions through their relationship to the central charges of the SCFT. This relationship of the stratification data to the central charges is used here, but is derived and explained in a companion paper by one of the authors. We illustrate the use of these conditions by re-analyzing many previously-known examples of rank 2 SCFTs, and also by finding examples of new theories. The power of these conditions stems from the fact that for Coulomb branch stratifications a conjecturally complete list of physically allowed elementary slices is known. By contrast, constraining the possible elementary slices of symplectic singularities relevant for Higgs branch stratifications remains an open problem.
A symplectically invariant definition of special Kahler geometry is discussed. Certain aspects hereof are illustrated by means of Calabi-Yau moduli spaces.
We study generalized Kahler structures on N = (2, 2) supersymmetric Wess-Zumino-Witten models; we use the well known case of SU(2) x U(1) as a toy model and develop tools that allow us to construct the superspace action and uncover the highly nontrivial structure of the hitherto unexplored case of SU(3); these tools should be useful for studying many other examples. We find that different generalized Kahler structures on N = (2, 2) supersymmetric Wess-Zumino-Witten models can be found by T-duality transformations along affine isometries.
We propose a graph-based approach to 5d superconformal field theories (SCFTs) based on their realization as M-theory compactifications on singular elliptic Calabi--Yau threefolds. Field-theoretically, these 5d SCFTs descend from 6d $mathcal{N}=(1,0)$ SCFTs by circle compactification and mass deformations. We derive a description of these theories in terms of graphs, so-called Combined Fiber Diagrams, which encode salient features of the partially resolved Calabi--Yau geometry, and provides a combinatorial way of characterizing all 5d SCFTs that descend from a given 6d theory. Remarkably, these graphs manifestly capture strongly coupled data of the 5d SCFTs, such as the superconformal flavor symmetry, BPS states, and mass deformations. The capabilities of this approach are demonstrated by deriving all rank one and rank two 5d SCFTs. The full potential, however, becomes apparent when applied to theories with higher rank. Starting with the higher rank conformal matter theories in 6d, we are led to the discovery of previously unknown flavor symmetry enhancements and new 5d SCFTs.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
