We compute the 4d superconformal index for N=1, 2 gauge theories on S1×L(p,1), where L(p,1) is a lens space. We find that the 4d N=1, 2 index on S1×L(p,1) reduces to a 3d N=2, 4 index on S1×S2 in the large p limit, and to a 3d partition function on a squashed L(p,1) when the size of the temporal S1 shrinks to zero. As an application of our index, we study 4d N=2 superconformal field theories arising from the 6d N=(2,0) A1 theory on a punctured Riemann surface Σ, and conjecture the existence of a 2d topological quantum field theory on Σ whose correlation function coincides with the 4d N=2 index on S1×L(p,1).

4d index to 3d index and 2d topological quantum field theory / Benini, F.; Nishioka, T.; Yamazaki, M.. - In: PHYSICAL REVIEW D, PARTICLES, FIELDS, GRAVITATION, AND COSMOLOGY. - ISSN 1550-7998. - 86:6(2012), pp. 065015.1-065015.10. [10.1103/PhysRevD.86.065015]

4d index to 3d index and 2d topological quantum field theory

Benini, F.;
2012-01-01

Abstract

We compute the 4d superconformal index for N=1, 2 gauge theories on S1×L(p,1), where L(p,1) is a lens space. We find that the 4d N=1, 2 index on S1×L(p,1) reduces to a 3d N=2, 4 index on S1×S2 in the large p limit, and to a 3d partition function on a squashed L(p,1) when the size of the temporal S1 shrinks to zero. As an application of our index, we study 4d N=2 superconformal field theories arising from the 6d N=(2,0) A1 theory on a punctured Riemann surface Σ, and conjecture the existence of a 2d topological quantum field theory on Σ whose correlation function coincides with the 4d N=2 index on S1×L(p,1).
2012
86
6
1
10
065015
https://journals.aps.org/prd/abstract/10.1103/PhysRevD.86.065015
https://arxiv.org/abs/1109.0283
Benini, F.; Nishioka, T.; Yamazaki, M.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/32431
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