Witten index for noncompact dynamics

  • Seung-Joo Lee
  • Piljin YiEmail author
Open Access
Regular Article - Theoretical Physics


Among gauged dynamics motivated by string theory, we find many with gapless asymptotic directions. Although the natural boundary condition for ground states is L 2, one often turns on chemical potentials or supersymmetric mass terms to regulate the infrared issues, instead, and computes the twisted partition function. We point out how this procedure generically fails to capture physical L 2 Witten index with often misleading results. We also explore how, nevertheless, the Witten index is sometimes intricately embedded in such twisted partition functions. For d = 1 theories with gapless continuum sector from gauge multiplets, such as non-primitive quivers and pure Yang-Mills, a further subtlety exists, leading to fractional expressions. Quite unexpectedly, however, the integral L 2 Witten index can be extracted directly and easily from the twisted partition function of such theories. This phenomenon is tied to the notion of the rational invariant that appears naturally in the wall-crossing formulae, and offers a general mechanism of reading off Witten index directly from the twisted partition function. Along the way, we correct early numerical results for some of \( \mathcal{N} \) = 4, 8, 16 pure Yang-Mills quantum mechanics, and count threshold bound states for general gauge groups beyond SU(N ).


Extended Supersymmetry Supersymmetry and Duality D-branes M(atrix) Theories 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.Department of PhysicsRobeson Hall, Virginia TechBlacksburgU.S.A.
  2. 2.School of Physics and Quantum Universe CenterKorea Institute for Advanced StudySeoulKorea

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