SciPost Submission Page
Line Operators in 4d Chern-Simons Theory and Cherkis Bows
by Nafiz Ishtiaque, Yehao Zhou
Submission summary
| Authors (as registered SciPost users): | Nafiz Ishtiaque |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2211.00049v4 (pdf) |
| Date accepted: | Feb. 6, 2024 |
| Date submitted: | Jan. 17, 2024, 5:56 a.m. |
| Submitted by: | Nafiz Ishtiaque |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approach: | Theoretical |
Abstract
We show that the phase spaces of a large family of line operators in 4d Chern-Simons theory with $\text{GL}_n$ gauge group are given by Cherkis bow varieties with $n$ crosses. These line operators are characterized by Hanany-Witten type brane constructions involving D3, D5, and NS5 branes in an $\Omega$-background. Linking numbers of the five-branes and mass parameters for the D3 brane theories determine the phase spaces and in special cases they correspond to vacuum moduli spaces of 3d $\mathcal{N}=4$ quiver theories. Examples include line operators that conjecturally create T, Q, and L-operators in integrable spin chains.
List of changes
Based on the last referee report: 1. New citation added for existing result relating bow equations to the vacuum equations of 4d N=4 with impurity walls (second paragraph, p. 3). 2. References cited for: a) The result that 2d B-model with superpotential W localizes to 0d theory with action W upon omega deformation, concerning eq. 4.46. b) Quantization of $gl_n^*$ to the universal enveloping algebra $U_\hbar(gl_n)$ upon turning on twisted masses (paragraph containing eq. 5.5). c) Localization of 3d N=4 theory to topological quantum mechanics by omega deformation (second paragraph of section 2.1). 3. In the second paragraph on p.2: The statement regarding coupling a quantum mechanics with global symmetry to a gauge theory changed slightly to make it clearer. 4. Support of $\vec \omega$ corrected after eq. 2.1. 5. Mentioned $K_i$ and $L_p$ to be integers, before eq. 2.2. 6. Spelled out the meaning of "unsymmetrization" in Remark 5.3. 7. Corrected several spelling errors.
Published as SciPost Phys. 16, 052 (2024)