A few Ricci-flat stacks as phases of exotic GLSM's

GLSM's for gerbes (and other toric stacks)

In this paper we will discuss gauged linear sigma model descriptions of toric stacks. Toric stacks have a simple description in terms of (symplectic, GIT) ${\bf C}^{\times}$ quotients of homogeneous coordinates, in exactly the same form as toric varieties. We describe the physics of the gauged linear sigma models that formally coincide with the mathematical description of toric stacks, and check that physical predictions of those gauged linear sigma models exactly match the corresponding stacks. We also check in examples that when a given toric stack has multiple presentations in a form access…

Non-birational twisted derived equivalences in abelian GLSMs

In this paper we discuss some examples of abelian gauged linear sigma models realizing twisted derived equivalences between non-birational spaces, and realizing geometries in novel fashions. Examples of gauged linear sigma models with non-birational Kahler phases are a relatively new phenomenon. Most of our examples involve gauged linear sigma models for complete intersections of quadric hypersurfaces, though we also discuss some more general cases and their interpretation. We also propose a more general understanding of the relationship between Kahler phases of gauged linear sigma models, nam…

GLSM's, gerbes, and Kuznetsov's homological projective duality

In this short note we give an overview of recent work on string propagation on stacks and applications to gauged linear sigma models. We begin by outlining noneffective orbifolds (orbifolds in which a subgroup acts trivially) and related phenomena in two-dimensional gauge theories, which realize string propagation on gerbes. We then discuss the `decomposition conjecture,' equating conformal field theories of strings on gerbes and strings on disjoint unions of spaces. Finally, we apply these ideas to gauged linear sigma models for complete intersections of quadrics, and use the decomposition co…

无RG流的规范线性σ模型产生的里奇平坦度量

Ricci-flat metrics from gauged linear $σ$-models without RG flow

该研究利用带不定号的规范线性σ模型（GLSMs）引入影子坐标，构造出广义锥上的里奇平坦凯勒度量，给出凯勒势通用公式，为卡拉比-丘度量和环面几何研究提供新方向。

Local D3/D7 mu-Split SUSY, 125 GeV Higgs and Large Volume Ricci-Flat Swiss-Cheese Metrics: A Brief Review

In this article, we review briefly recent progress made in realizing local(ized around a mobile space-time filling D3-brane in) D3/D7 mu-Split Supersymmetry in (the large volume limit of Type IIB) String Theory (compactified on Swiss-Cheese Calabi-Yau orientifolds) as well as obtaining a 125 GeV (light) Higgs in the same set up. We also discuss obtaining the geometric Kaehler potential (and hence the Ricci-Flat metric) for the Swiss-Cheese Calabi-Yau in the large volume limit using the Donaldson's algorithm and intuition from GLSM-based calculations - we present new results for Swiss-Cheese Ca…

A new Ricci flat geometry

We are proposing a new Ricci flat metric constructed from an infinite family of Sasaki-Einstein, $Y^{(p,q)}$, geometries. This geometry contains a free parameter $s$ and in the $s\to 0$ limit we get back the usual CY. When this geometry is probed both by a stack of D3 and fractional D3 branes then the corresponding supergravity solution is found which is a warped product of this new 6-dimensional geometry and the flat $R^{3,1}$. This solution in the specific limit as mentioned above reproduces the solution found in hep-th/0412193. The integrated five-form field strength over $S^2\times S^3$ go…