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Title: The long flow to freedom

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. As a result, we expect a similar qualitative behavior alsomore » for other non-compact sigma models, even when they do not flow to free theories.« less

Authors:
 [1];  [2];  [3];  [4]
  1. Weizmann Institute of Science, Rehovot (Israel)
  2. Technion, Haifa (Israel)
  3. Institute for Advanced Study, Princeton, NJ (United States)
  4. Univ. of California, Santa Barbara, CA (United States)
Publication Date:
Research Org.:
Univ. of California, San Diego, CA (United States); Weizmann Institute of Science, Rehovot (Israel)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
OSTI Identifier:
1356084
Alternate Identifier(s):
OSTI ID: 1358379
Grant/Contract Number:
SC0009988
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 2; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; renormalization group; supersymmetric gauge theory; supersymmetry and duality; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Aharony, Ofer, Razamat, Shlomo S., Seiberg, Nathan, and Willett, Brian. The long flow to freedom. United States: N. p., 2017. Web. doi:10.1007/JHEP02(2017)056.
Aharony, Ofer, Razamat, Shlomo S., Seiberg, Nathan, & Willett, Brian. The long flow to freedom. United States. doi:10.1007/JHEP02(2017)056.
Aharony, Ofer, Razamat, Shlomo S., Seiberg, Nathan, and Willett, Brian. Fri . "The long flow to freedom". United States. doi:10.1007/JHEP02(2017)056. https://www.osti.gov/servlets/purl/1356084.
@article{osti_1356084,
title = {The long flow to freedom},
author = {Aharony, Ofer and Razamat, Shlomo S. and Seiberg, Nathan and Willett, Brian},
abstractNote = {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. As a result, we expect a similar qualitative behavior also for other non-compact sigma models, even when they do not flow to free theories.},
doi = {10.1007/JHEP02(2017)056},
journal = {Journal of High Energy Physics (Online)},
number = 2,
volume = 2017,
place = {United States},
year = {Fri Feb 10 00:00:00 EST 2017},
month = {Fri Feb 10 00:00:00 EST 2017}
}

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Free Publicly Available Full Text
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Cited by: 7works
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  • 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 minusmore » 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.« less
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