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

Ievlev, E.; Shifman, M.; Yung, A.

doi:10.1103/physrevd.102.054026

Title: 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:

; Shifman, M.;

Publication Date:: Tue Sep 29 00:00:00 EDT 2020

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.  doi:10.1103/physrevd.102.054026.

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                    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

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                    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.

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@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         = {Tue Sep 29 00:00:00 EDT 2020},

  month        = {Tue Sep 29 00:00:00 EDT 2020}

}

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

Abstract

Citation Formats

Lessons from supersymmetry: "Instead-of-confinement" mechanism journal, October 2014

Phases of N = 2 theories in two dimensions journal, August 1993

Non-Abelian string junctions as confined monopoles journal, August 2004

Solitons in the Higgs phase: the moduli matrix approach journal, June 2006

On classification ofN=2 supersymmetric theories journal, December 1993

Vortices, instantons and branes journal, July 2003

The BPS spectra of gauge theories in two and four dimensions journal, May 1999

Studying critical string emerging from non-Abelian vortex in four dimensions journal, August 2016

Vortex Strings and Four-Dimensional Gauge Dynamics journal, April 2004

Critical string from non-Abelian vortex in four dimensions journal, November 2015

Quantum vortex strings: A review journal, January 2009

Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD journal, December 1994

Spontaneously broken supergauge symmetries and goldstone spinors journal, September 1974

Instatons, the quark model, and the 1/N expansion journal, March 1979

Non-Abelian duality and confinement in N = 2 supersymmetric QCD journal, June 2009

New phenomena in SU(3) supersymmetric gauge theory journal, August 1995

An effective action for the supersymmetric CPn−1 model journal, July 1983

The moduli space of vacua of N = 2 SUSY QCD and duality in N = 1 SUSY QCD journal, July 1996

Supergravity and a confining gauge theory: duality cascades and χSB-resolution of naked singularities journal, August 2000

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Non-Abelian confinement in N = 2 supersymmetric QCD: Duality and kinks on confining strings journal, April 2010

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Quantum fluctuations of instantons in the nonlinear σ model journal, July 1979

Branes and N = 2 theories in two dimensions journal, March 1998

Generalized Calabi-Yau compactifications with D-branes and fluxes journal, July 2005

Effective world-sheet theory for non-Abelian semilocal strings in N = 2 supersymmetric QCD journal, June 2011

The BPS spectra of two-dimensional supersymmetric gauge theories with twisted mass terms journal, November 1998

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Comments on conifolds journal, September 1990

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New vortex-string worldsheet theories from supersymmetric localization journal, March 2019

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New = 2 superconformal field theories in four dimensions journal, February 1996

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r Duality and “instead-of-confinement” mechanism in N = 1 supersymmetric QCD journal, July 2012

Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory journal, September 1994

Nonabelian superconductors: vortices and confinement in SQCD journal, November 2003

An effective lagrangian for the pure N = 1 supersymmetric Yang-Mills theory journal, June 1982

Coulomb Phase of N = 2 Supersymmetric QCD journal, August 1995

Non-Abelian vortex in four dimensions as a critical string on a conifold journal, September 2016

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Non-Abelian string junctions as confined monopoles
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On classification ofN=2 supersymmetric theories
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Vortices, instantons and branes
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The BPS spectra of gauge theories in two and four dimensions
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Studying critical string emerging from non-Abelian vortex in four dimensions
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Instatons, the quark model, and the 1/N expansion
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Quantum dynamics of low-energy theory on semilocal non-Abelian strings
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Quantum fluctuations of instantons in the nonlinear σ model
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Branes and N = 2 theories in two dimensions
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Generalized Calabi-Yau compactifications with D-branes and fluxes
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Effective world-sheet theory for non-Abelian semilocal strings in $N = 2$ supersymmetric QCD
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The BPS spectra of two-dimensional supersymmetric gauge theories with twisted mass terms
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Deformation of conifold and intersecting branes
journal, February 2000

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Comments on conifolds
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An effective lagrangian for the pure N = 1 supersymmetric Yang-Mills theory
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