Supersymmetric reduction of 3D theories on a line segment

Mykola Dedushenko (Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, New York 11794-3636, USA) ; Mikhail Litvinov (Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794-3800, USA and C. N. Yang Institute for Theoretical Physics, Stony Brook University, Stony Brook, New York 11794-3800, USA)

We study three-dimensional quantum field theories on the interval with symmetry-preserving boundary conditions. The physics and symmetries of the effective 2D theory in the IR are the main subjects of this note. We focus on the (super-)Yang-Mills-Chern-Simons (YM-CS) theories with the Dirichlet boundary conditions on both ends. We warm up with the N=0 and N=1 cases flowing to the bosonic and N=(0,1) WZW models in 2D. Then we study the 3D N=2 YM-CS on the interval with the N=(0,2) Dirichlet boundaries. It flows to a noncompact version of the N=(0,2) WZW. We compute its perturbatively exact two-derivative effective action (i.e., the metric and the B-field), and speculate on the possibility of novel nonperturbative effects. We also construct the 2D Landau-Ginzburg models flowing to the similar sigma models.

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      "source": "APS", 
      "value": "We study three-dimensional quantum field theories on the interval with symmetry-preserving boundary conditions. The physics and symmetries of the effective 2D theory in the IR are the main subjects of this note. We focus on the (super-)Yang-Mills-Chern-Simons (YM-CS) theories with the Dirichlet boundary conditions on both ends. We warm up with the <math><mi>N</mi><mo>=</mo><mn>0</mn></math> and <math><mi>N</mi><mo>=</mo><mn>1</mn></math> cases flowing to the bosonic and <math><mi>N</mi><mo>=</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math> WZW models in 2D. Then we study the 3D <math><mi>N</mi><mo>=</mo><mn>2</mn></math> YM-CS on the interval with the <math><mi>N</mi><mo>=</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>)</mo></math> Dirichlet boundaries. It flows to a noncompact version of the <math><mi>N</mi><mo>=</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>)</mo></math> WZW. We compute its perturbatively exact two-derivative effective action (i.e., the metric and the B-field), and speculate on the possibility of novel nonperturbative effects. We also construct the 2D Landau-Ginzburg models flowing to the similar sigma models."
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Published on:
25 August 2023
Publisher:
APS
Published in:
Physical Review D , Volume 108 (2023)
Issue 4
DOI:
https://doi.org/10.1103/PhysRevD.108.045016
arXiv:
2212.07455
Copyrights:
Published by the American Physical Society
Licence:
CC-BY-4.0

Fulltext files: