4d Index to 3d Index and 2d TQFT

By F. Benini, T. Nishioka, Masahito Yamazaki. 2011

169 citations recorded by the source corpus.

We compute the 4d superconformal index for N = 1, 2 gauge theories on S × L(p, 1), where L(p, 1) is a lens space. We find that the 4d N = 1, 2 index on S × L(p, 1) reduces to a 3d N = 2, 4 index on S × S in the large p limit, and to a 3d partition function on a squashed L(p, 1) when the size of the temporal S 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 S × L(p, 1).

Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/97cb1e29ef8271c16b9c978b6f80037ed8d1e074

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Citations in the corpus

Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS5 black holes (2018, methodology): “(8)The computations of [53, 54] rely on a nice technique presented in [56] which identifies a path integral representation of twisted generalizations of Witten’s index.”
Seiberg-Witten theories on ellipsoids (2012, result): “Similar exact results have also been obtained for 3D N ≥ 2 gauge theories on round three-sphere [3, 4, 5], its orbifold [6, 7], and 2D theories on sphere [8, 9].”
Localization techniques in quantum field theories (2016, methodology): “The appropriate background fields reside in the new minimal supergravity multiplet [35, 36],”
The geometry of supersymmetric partition functions (2013, background): “Four-dimensional N = 1 theories on L(r, 1) × S1 were studied in [65, 66].”
5-dim superconformal index with enhanced En global symmetry (2012, background): “of scalar vev of the vector multiplet, from our index, which is analogous to the cases of 4d to 3d reduction considered in [51, 54, 52, 53] where 3d Chern-Simons terms cannot be obtained under the reduction.”
N=1 theories of class S_k (2015, unknown): “One can also try and compute other partition functions, such as lens index [54], for class Sk theories.”
Partition Functions of $${\mathcal{N}=(2,2)}$$N=(2,2) Gauge Theories on S2 and Vortices (2012, methodology): “A longer version of this paper is available online [25], where we present more examples, some consistency checks with mirror symmetry, and a comparison with the threedimensional matrix integral for lens spaces L(p, 1) [13,15] in the p → ∞ limit, and with the three-dimensional integral for the index ”
A topologically twisted index for three-dimensional supersymmetric theories (2015, background): “As first observed in [14] and later elaborated upon in [15, 16], both the S3 partition function of [29], the S2×S1 supersymmetric index of [47, 48] and the lens space index of [49] “factorize” into building elements which can be interpreted as the partition function on R(2)Ω×S(1) in an Ω-background.”
N$$ \mathcal{N} $$ = 1 supersymmetric indices and the four-dimensional A-model (2017, background): “However, the background we consider here differs from that considered in [42] for p > 2 due to the presence of a non-trivial R-symmetry gauge field.”