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## Long Way to Ricci Flatness

We study two-dimensional weighted N = (2; 2) supersymmetric CP models

with the goal of exploring their infrared (IR) limit. WCP(N, tildeN) are simplifed 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, tildeN) has N charges +1 and tilde N

charges -1 fields. As well-known, at e N = tildeN 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) ow 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.