A new pentagon identity for the tetrahedron index

Gahramanov, Ilmar; Rosengren, Hjalmar

doi:10.1007/jhep11(2013)128

Cited by 25 publications

(47 citation statements)

References 69 publications

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“…More recently it has been called new pentagon identity and plays a role in the study of shaped triangulations, [32]. This identity can also be obtained as a particular limit of the elliptic beta-integral discovered by Spiridonov [33] and has been tested also on the 3d index [34].…”

Section: Jhep08(2016)136mentioning

confidence: 99%

3d N $$ \mathcal{N} $$ = 2 mirror symmetry, pq-webs and monopole superpotentials

Benvenuti

Pasquetti

2016

J. High Energ. Phys.

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D3 branes stretching between webs of (p,q) 5branes provide an interesting class of 3d N = 2 theories. For generic pq-webs however the low energy field theory is not known. We use 3d mirror symmetry and Type IIB S-duality to construct Abelian gauge theories corresponding to D3 branes ending on both sides of a pq-web made of many coincident N S5's intersecting one D5. These theories contain chiral monopole operators in the superpotential and enjoy a non trivial pattern of global symmetry enhancements. In the special case of the pq-web with one D5 and one N S5, the 3d low energy SCFT admits three dual formulations. This triality can be applied locally inside bigger quiver gauge theories. We prove our statements using partial mirror symmetryà la Kapustin-Strassler, showing the equality of the S 3 b partition functions and studying the quantum chiral rings.

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Section: Jhep08(2016)136mentioning

confidence: 99%

3d N $$ \mathcal{N} $$ = 2 mirror symmetry, pq-webs and monopole superpotentials

Benvenuti

Pasquetti

2016

J. High Energ. Phys.

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“…Then the integral identity (8) can be written as a pentagon identity [39,13,32,8] Another simple but more interesting example of the pentagon identity is provided by the equality of RP 2 × S 1 partition functions. According to the mirror symmetry we have the following integral identity [40,41,42]…”

Section: Pentagon Identitiesmentioning

confidence: 99%

“…A typical example of the pentagon identity arising from the supersymmetric gauge theories is the equality of the partition functions of three-dimensional N = 2 mirror dual theories which has the following arXiv:1803.00855v1 [math-ph] 2 Mar 2018 form [10,11,12,13,3,8,14] dµ…”

Section: Introductionmentioning

confidence: 99%

Pentagon Identities Arising in Supersymmetric Gauge Theory Computations

Bozkurt

Gahramanov

2019

Theor Math Phys

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The partition functions of three-dimensional N = 2 supersymmetric gauge theories on different manifolds can be expressed as q-hypergeometric integrals. By comparing the partition functions of three-dimensional mirror dual theories, one finds complicated integral identities. In some cases, these identities can be written in the form of pentagon relations. Such identities often have an interpretation as the Pachner's 3-2 move for triangulated manifolds via the so-called 3d-3d correspondence. From the physics perspective, another important application of pentagon identities is that they may be used to construct new solutions to the quantum Yang-Baxter equation.

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“…We then have the biorthogonality relations J(Q (i, j) n Q ( j,i) m ) = 0 for m = n. We may assume that i = 5, j = 6. Then, Q (5,6) n is given by the function (our notation differs from that of Rahman) More precisely, Rahman proved that if…”

Section: Rahman's Biorthogonal Functionsmentioning

confidence: 99%

“…In a similar way, one can obtain basic hypergeometric integrals from three-dimensional theories [6,7,11,12,14,19,41]. Interestingly, the resulting integrals are not of a type considered in the classical literature but involve a mixture of continuous and discrete integration (this can also happen for four-dimensional theories [16,33], but then with a finite rather than infinite discrete component).…”

Section: Introductionmentioning

confidence: 99%

Rahman’s Biorthogonal Rational Functions and Superconformal Indices

Rosengren

2017

Constr Approx

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We study biorthogonal functions related to basic hypergeometric integrals with coupled continuous and discrete components. Such integrals appear as superconformal indices for three-dimensional quantum field theories and also in the context of solvable lattice models. We obtain explicit biorthogonal systems given by products of two of Rahman's biorthogonal rational 10 W 9 -functions or their degenerate cases. We also give new bilateral extensions of the Jackson and q-Saalschütz summation formulas and new continuous and discrete biorthogonality measures for Rahman's functions.

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A new pentagon identity for the tetrahedron index

Cited by 25 publications

References 69 publications

3d N $$ \mathcal{N} $$ = 2 mirror symmetry, pq-webs and monopole superpotentials

3d N $$ \mathcal{N} $$ = 2 mirror symmetry, pq-webs and monopole superpotentials

Pentagon Identities Arising in Supersymmetric Gauge Theory Computations

Rahman’s Biorthogonal Rational Functions and Superconformal Indices

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