[Paper Review] T[U(N)] duality webs: mirror symmetry, spectral duality and gauge/CFT correspondences

Anton Nedelin Sara Pasquetti Yegor Zenkevich|arXiv (Cornell University)|Dec 21, 2017

Black Holes and Theoretical Physics65 references12 citations

TL;DR

This paper establishes a duality web connecting 3d FT[SU(N)] theories, 3d spectral duals, and q-Toda conformal blocks via partition functions, demonstrating that the FT[SU(N)] partition function arises from Higgsing a 5d linear quiver or from refined topological strings on a toric Calabi-Yau threefold. A key result is a new direct map between the 2d FT[SU(N)] GLSM partition function and an (N+2)-point Toda conformal block.

ABSTRACT

We study various duality webs involving the 3d FT[SU(N)] theory, a close relative of the T[SU(N)] quiver tail. We first map the partition functions of FT[SU(N)] and its 3d spectral dual to a pair of spectral dual q-Toda conformal blocks. Then we show how to obtain the FT[SU(N)] partition function by Higgsing a 5d linear quiver gauge theory, or equivalently from the refined topological string partition function on a certain toric Calabi-Yau three-fold. 3d spectral duality in this context descends from 5d spectral duality. Finally we discuss the 2d reduction of the 3d spectral dual pair and study the corresponding limits on the q-Toda side. In particular we obtain a new direct map between the partition function of the 2d FT[SU(N)] GLSM and an (N+2)-point Toda conformal block.

Motivation & Objective

• To establish a duality web linking 3d FT[SU(N)] theories, their 3d spectral duals, and q-Toda conformal blocks.
• To demonstrate that the FT[SU(N)] partition function can be derived from Higgsing a 5d linear quiver gauge theory.
• To show that the 3d spectral duality arises from 5d spectral duality in the context of refined topological strings.
• To study the 2d reduction of the 3d spectral dual pair and its implications for conformal block maps.
• To construct a new direct correspondence between the 2d FT[SU(N)] GLSM partition function and an (N+2)-point Toda conformal block.

Proposed method

• Mapping the partition functions of FT[SU(N)] and its 3d spectral dual to a pair of spectral dual q-Toda conformal blocks.
• Using Higgsing procedures to derive the FT[SU(N)] partition function from a 5d linear quiver gauge theory.
• Relating the partition function to the refined topological string partition function on a specific toric Calabi-Yau threefold.
• Deriving 3d spectral duality from the underlying 5d spectral duality structure.
• Reducing the 3d spectral dual pair to 2d and analyzing the resulting limits on the q-Toda side.
• Constructing a new direct map between the 2d FT[SU(N)] GLSM partition function and an (N+2)-point Toda conformal block.

Experimental results

Research questions

• RQ1 How are the partition functions of FT[SU(N)] and its 3d spectral dual related to q-Toda conformal blocks?
• RQ2 Can the FT[SU(N)] partition function be obtained via Higgsing a 5d linear quiver gauge theory?
• RQ3 What is the origin of 3d spectral duality in terms of 5d spectral duality?
• RQ4 How does the 2d reduction of the 3d spectral dual pair manifest on the q-Toda side?
• RQ5 Is there a direct correspondence between the 2d FT[SU(N)] GLSM partition function and a higher-point Toda conformal block?

Key findings

• The partition functions of FT[SU(N)] and its 3d spectral dual are mapped to a pair of spectral dual q-Toda conformal blocks.
• The FT[SU(N)] partition function is successfully obtained by Higgsing a 5d linear quiver gauge theory.
• The 3d spectral duality is shown to descend from 5d spectral duality in the refined topological string framework.
• The 2d reduction of the 3d spectral dual pair leads to a new direct map between the 2d FT[SU(N)] GLSM partition function and an (N+2)-point Toda conformal block.
• The refined topological string partition function on a specific toric Calabi-Yau threefold reproduces the FT[SU(N)] partition function.
• The spectral duality structure is preserved under dimensional reduction, enabling new conformal block correspondences.