TY - JOUR

T1 - Long way to Ricci flatness

AU - Chen, Jin

AU - Sheu, Chao Hsiang

AU - Shifman, Mikhail

AU - Tallarita, Gianni

AU - Yung, Alexei

N1 - Publisher Copyright:
© 2020, The Author(s).

PY - 2020/10/1

Y1 - 2020/10/1

N2 - We study two-dimensional weighted N = (2) supersymmetric ℂℙ models with the goal of exploring their infrared (IR) limit. Wℂℙ(N,N˜) are simplified versions of world-sheet theories on non-Abelian strings in four-dimensional N = 2 QCD. In the gauged linear sigma model (GLSM) formulation, Wℂℙ(N,N˜) has N charges +1 and N˜ charges −1 fields. As well-known, at N˜ = N this GLSM is conformal. Its target space is believed to be a non-compact Calabi-Yau manifold. We mostly focus on the N = 2 case, then the Calabi-Yau space is a conifold. On the other hand, in the non-linear sigma model (NLSM) formulation the model has ultra-violet logarithms and does not look conformal. Moreover, its metric is not Ricci-flat. We address this puzzle by studying the renormalization group (RG) flow of the model. We show that the metric of NLSM becomes Ricci-flat in the IR. Moreover, it tends to the known metric of the resolved conifold. We also study a close relative of the Wℂℙ model — the so called zn model — which in actuality represents the world sheet theory on a non-Abelian semilocal string and show that this zn model has similar RG properties.

AB - We study two-dimensional weighted N = (2) supersymmetric ℂℙ models with the goal of exploring their infrared (IR) limit. Wℂℙ(N,N˜) are simplified versions of world-sheet theories on non-Abelian strings in four-dimensional N = 2 QCD. In the gauged linear sigma model (GLSM) formulation, Wℂℙ(N,N˜) has N charges +1 and N˜ charges −1 fields. As well-known, at N˜ = N this GLSM is conformal. Its target space is believed to be a non-compact Calabi-Yau manifold. We mostly focus on the N = 2 case, then the Calabi-Yau space is a conifold. On the other hand, in the non-linear sigma model (NLSM) formulation the model has ultra-violet logarithms and does not look conformal. Moreover, its metric is not Ricci-flat. We address this puzzle by studying the renormalization group (RG) flow of the model. We show that the metric of NLSM becomes Ricci-flat in the IR. Moreover, it tends to the known metric of the resolved conifold. We also study a close relative of the Wℂℙ model — the so called zn model — which in actuality represents the world sheet theory on a non-Abelian semilocal string and show that this zn model has similar RG properties.

KW - Renormalization Group

KW - Sigma Models

KW - Supersymmetric Gauge Theory

UR - http://www.scopus.com/inward/record.url?scp=85092315299&partnerID=8YFLogxK

U2 - 10.1007/JHEP10(2020)059

DO - 10.1007/JHEP10(2020)059

M3 - Article

AN - SCOPUS:85092315299

SN - 1126-6708

VL - 2020

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 10

M1 - 59

ER -