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
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
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
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
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
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
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
$\DeclareMathOperator\Spin{Spin}\DeclareMathOperator\SL{SL}\DeclareMathOperator\SU{SU}$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
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
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
