# String baryon in four-dimensional N=2 supersymmetric QCD from the 2D-4D correspondence

## Abstract

We study non-Abelian vortex strings in four-dimensional (4D) $$\mathscr{N}=2$$ supersymmetric QCD with the $U(N=2)$ gauge group and $$N_f=4$$ flavors of quark hypermultiplets. It has recently been shown that these vortices behave as critical superstrings. The spectrum of closed string states in the associated string theory was found and interpreted as a spectrum of hadrons in 4D $$\mathscr{N}=2$$ supersymmetric QCD. In particular, the lowest string state appears to be a massless Bogomol’nyi-Prasad-Sommerfield (BPS) “baryon.” Here we show the occurrence of this stringy baryon using a purely field-theoretic method. To this end we study the conformal world-sheet theory on the non-Abelian string—the so-called weighted $$\mathscr{N}=(2,2)$$ supersymmetric $$\mathbb{CP}$$ model. Its target space is given by the six-dimensional noncompact Calabi-Yau space $$Y_6$$, the conifold. We use a mirror description of the model to study the BPS kink spectrum and its transformations on curves (walls) of marginal stability. Then we use the 2D-4D correspondence to show that the deformation of the complex structure of the conifold is associated with the emergence of a nonperturbative Higgs branch in 4D theory which opens up at strong coupling. The modulus parameter on this Higgs branch is the vacuum expectation value of the massless BPS baryon previously found in string theory.

- Authors:

- Publication Date:

- Research Org.:
- Univ. of Minnesota, Minneapolis, MN (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP); Russian Foundation for Basic Research; Foundation for the Advancement of Theoretical Physics and Mathematics; Theoretical Physics and Mathematics Advancement Foundation (BASIS) (Russian Federation)

- OSTI Identifier:
- 1668447

- Alternate Identifier(s):
- OSTI ID: 1705074

- Grant/Contract Number:
- SC0011842; 18-02-00048a; 19-1-5-106-1

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 102 Journal Issue: 5; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; bound states; color confinement; effective field theory; gauge theories; nonperturbative effects in field theory; sigma models; supersymmetric field theories

### Citation Formats

```
Ievlev, E., Shifman, M., and Yung, A. String baryon in four-dimensional N=2 supersymmetric QCD from the 2D-4D correspondence. United States: N. p., 2020.
Web. https://doi.org/10.1103/physrevd.102.054026.
```

```
Ievlev, E., Shifman, M., & Yung, A. String baryon in four-dimensional N=2 supersymmetric QCD from the 2D-4D correspondence. United States. https://doi.org/10.1103/physrevd.102.054026
```

```
Ievlev, E., Shifman, M., and Yung, A. Tue .
"String baryon in four-dimensional N=2 supersymmetric QCD from the 2D-4D correspondence". United States. https://doi.org/10.1103/physrevd.102.054026.
```

```
@article{osti_1668447,
```

title = {String baryon in four-dimensional N=2 supersymmetric QCD from the 2D-4D correspondence},

author = {Ievlev, E. and Shifman, M. and Yung, A.},

abstractNote = {We study non-Abelian vortex strings in four-dimensional (4D) $\mathscr{N}=2$ supersymmetric QCD with the $U(N=2)$ gauge group and $N_f=4$ flavors of quark hypermultiplets. It has recently been shown that these vortices behave as critical superstrings. The spectrum of closed string states in the associated string theory was found and interpreted as a spectrum of hadrons in 4D $\mathscr{N}=2$ supersymmetric QCD. In particular, the lowest string state appears to be a massless Bogomol’nyi-Prasad-Sommerfield (BPS) “baryon.” Here we show the occurrence of this stringy baryon using a purely field-theoretic method. To this end we study the conformal world-sheet theory on the non-Abelian string—the so-called weighted $\mathscr{N}=(2,2)$ supersymmetric $\mathbb{CP}$ model. Its target space is given by the six-dimensional noncompact Calabi-Yau space $Y_6$, the conifold. We use a mirror description of the model to study the BPS kink spectrum and its transformations on curves (walls) of marginal stability. Then we use the 2D-4D correspondence to show that the deformation of the complex structure of the conifold is associated with the emergence of a nonperturbative Higgs branch in 4D theory which opens up at strong coupling. The modulus parameter on this Higgs branch is the vacuum expectation value of the massless BPS baryon previously found in string theory.},

doi = {10.1103/physrevd.102.054026},

journal = {Physical Review D},

number = 5,

volume = 102,

place = {United States},

year = {2020},

month = {9}

}

https://doi.org/10.1103/physrevd.102.054026

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