The long flow to freedom
arXiv:1611.02763 · doi:10.1007/JHEP02(2017)056
Abstract
Two-dimensional field theories do not have a moduli space of vacua. Instead, it is common that their low-energy behavior is a sigma model with a target space. When this target space is compact its renormalization group flow is standard. When it is non-compact the continuous spectrum of operators can change the qualitative behavior. Here we discuss two-dimensional gauge theories with N=(2,2) supersymmetry. We focus on two specific theories, for which we argue that they flow to free chiral multiplets at low energies: the U(1) gauge theory with one flavor (two chiral superfields with charges plus and minus one) and a non-zero Fayet-Iliopoulos term, and pure SU(N) gauge theories. We argue that the renormalization group flow of these theories has an interesting order of limits issue. Holding the position on the target space fixed, the space flattens out under the renormalization group. On the other hand, if we first go to infinity on the target space and then perform the renormalization group, we always have a non-trivial space, e.g. a cone with a deficit angle. We explain how to interpret low-energy dualities between theories with non-compact target spaces. We expect a similar qualitative behavior also for other non-compact sigma models, even when they do not flow to free theories.
14 pages
References in corpus (16)
- Phases of Theories In Two Dimensions
- Don't Panic! Closed String Tachyons in ALE Spacetimes
- Partition functions of N=(2,2) gauge theories on S^2 and vortices
- Elliptic genera of 2d N=2 gauge theories
- Exact Results in D=2 Supersymmetric Gauge Theories
- Elliptic genera of two-dimensional N=2 gauge theories with rank-one gauge groups
- Duality of the Fermionic 2d Black Hole and N=2 Liouville Theory as Mirror Symmetry
- Aspects of Non-Abelian Gauge Dynamics in Two-Dimensional N=(2,2) Theories
- Localized Tachyons and RG Flows
- Spacetime Energy Decreases under World-sheet RG Flow
- Cluster algebras from dualities of 2d N=(2,2) quiver gauge theories
- On Decay of K-theory
- Irreversibility of World-sheet Renormalization Group Flow
- Ricci flows and their integrability in two dimensions
- Duality In Two-Dimensional (2,2) Supersymmetric Non-Abelian Gauge Theories
- Renormalization group flows and continual Lie algebras
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