Seiberg-Witten theory in 4d is categorification of Seiberg-Witten in 3d

According to Gukov et al. in this 2017 paper Seiberg-Witten theory in 4d categorifies Seiberg-Witten theory in 3d. In what sense is this phrase mentioned? I know what the process of categorification is (e.g. how Khovanov homology categorifies Jones polynomial). What is the exact relation between the 3d and 4d versions of Seiberg-Witten theory and … Read more

Fierz like identity for ϵabcσaijσbklσcpq\epsilon_{abc}\sigma^a_{ij}\sigma^b_{kl}\sigma^c_{pq}

It is known that contracting over the vector indices of two Pauli matrix can be simplified to a bunch of delta functions. This is done via Fierz formula δabσaijσbkl=δijδkl−2ϵikϵjl=2δilδjk−δijδkl Here, a,b,c=1,2,3 are vector indices, and i,j,k,l=1,2 are spinor indices. Repeated indices are summed over. However, I would like to know whether there is a similar … Read more

Conformal group and cobordism

In this post, I am exploring my thoughts on the implementation of conformal symmetry group structure and cobordism relations. Namely, I like to know what has been done and explored in the past? on understanding the relations of (1). the bordism classes of d-manifold (in d-dimensions) endorsed with the conformal symmetry group structure of G, … Read more

Are vertex operator algebras ever conspiratorial?

I have a vertex operator algebra (VOA) $V$ with all niceness properties (unitary, rational, CFT type, etc). Its Lie algebra $\mathfrak{g} = V_1$ of spin-$1$ fields is large, and I understand how the spaces of low-spin fields decompose as $\mathfrak{g}$-irreps. I know that, for specific spins $r,s,t$ that I care about, the OPE of a … Read more

Bridgeland stability for restricted Kahler moduli?

Let X be a simply-connected, smooth, projective Calabi-Yau threefold. To my understanding, Bridgeland introduced stability conditions on triangulated categories to give a proper mathematical definition of the stringy Kahler moduli space (SKMS) from physics. Conjecturally, the classical (complexified) Kahler cone KX(C) of X gives an open chart on the SKMS around the large-volume limit. Coordinates … Read more

Inverse semigroups and partial symmetries

I recently ran across the idea of inverse semi-groups in the context of partial symmetries, where the symmetry only acts on part of the system and not the entire system (e.g., in quasi-crystals). My question is the following: in physics, we often consider field theories with internal global symmetries. For example, the usual $U(1)$ global … Read more

What is the value of the partition function of CFT on a compact conformal manifold?

Is the value of the partition function of a 2d CFT on a compact conformal manifold well defined? Or is there some kind of “anomaly” that makes it dependent on a bulk or some other kind of further structure (as for some 2+1-dimensional TQFTs)? If yes, are there formulas that compute it given some topology-dependent … Read more

Comparison between spinor representations in $\operatorname{SL}(2,\mathbb C)=\operatorname{Spin}(1,3)$ and $\operatorname{Spin}(4)$

$\DeclareMathOperator\Spin{Spin}\DeclareMathOperator\SL{SL}\DeclareMathOperator\SU{SU}$We know that $$ \Spin(1,3)=\SL(2,\mathbb C) $$ and $$ \Spin(4)=\SU(2) \times \SU(2). $$ The $\Spin(1,3)$ is the Lorentz version of Spin group, while $\Spin(4)$ is the Euclidean version of Spin group. The spinor representations of $\Spin(4)$ is essentially the spinor representation of $\Spin(4)=\SU(2) \times \SU(2)$ thus it is labeled by two components of spinors, each … Read more

Intuition for conformal nets

I was planning on reading the work of Arthur Bartels, Christopher L. Douglas and André Henriques on the 3-category of conformal nets as discussed in these papers: Coordinate-free nets, Conformal blocks, Fusion of defects, The 3-category and Dualizability. I wanted to know how the structure of a conformal net arises from the physical notion of … Read more

Derived geometry and theoretical physics

Is there any link between derived geometry and theoretical physics? for example with particle physics or quantum mechanics? Specifically something that included the obstruction bundle. If possible I would like to have some bibliographic references. Answer AttributionSource : Link , Question Author : exxxit8 , Answer Author : Community