An Index for 4 Dimensional Super Conformal Theories View Full Text


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Article Info

DATE

2007-06-06

AUTHORS

Justin Kinney, Juan Maldacena, Shiraz Minwalla, Suvrat Raju

ABSTRACT

We present a trace formula for an index over the spectrum of four dimensional superconformal field theories on S3 × time. Our index receives contributions from states invariant under at least one supercharge and captures all information – that may be obtained purely from group theory – about protected short representations in 4 dimensional superconformal field theories. In the case of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal N}=4$$\end{document} theory our index is a function of four continuous variables. We compute it at weak coupling using gauge theory and at strong coupling by summing over the spectrum of free massless particles in AdS5 × S5 and find perfect agreement at large N and small charges. Our index does not reproduce the entropy of supersymmetric black holes in AdS5, but this is not a contradiction, as it differs qualitatively from the partition function over supersymmetric states of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal N}=4$$\end{document} theory. We note that entropy for some small supersymmetric AdS5 black holes may be reproduced via a D-brane counting involving giant gravitons. For big black holes we find a qualitative (but not exact) agreement with the naive counting of BPS states in the free Yang Mills theory. In this paper we also evaluate and study the partition function over the chiral ring in the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal N}=4$$\end{document} Yang Mills theory. More... »

PAGES

209-254

References to SciGraph publications

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  • 2003-07-29. On stringy AdS5 × S5 and higher spin holography in JOURNAL OF HIGH ENERGY PHYSICS
  • 2006-01-23. Large N BPS states and emergent quantum gravity in JOURNAL OF HIGH ENERGY PHYSICS
  • 2003-04-23. Systematics of quarter BPS operators in 𝒩 = 4 SYM in JOURNAL OF HIGH ENERGY PHYSICS
  • 2000-11-21. Giant gravitons from holomorphic surfaces in JOURNAL OF HIGH ENERGY PHYSICS
  • 2004-02-03. Supersymmetric AdS5 black holes in JOURNAL OF HIGH ENERGY PHYSICS
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    82 state
    83 state invariants
    84 strong coupling
    85 supercharges
    86 superconformal field theories
    87 supersymmetric AdS5 black holes
    88 supersymmetric black holes
    89 supersymmetric states
    90 theory
    91 time
    92 trace formula
    93 variables
    94 weak coupling
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