Fetching the paper…

Reading the bibliography…

The superconformal index and an elliptic algebra of surface defects · Around

2014

The superconformal index and an elliptic algebra of surface defects

Bullimore, Mathew, Fluder, Martin, Hollands, Lotte et al.

Original
PDF
Post on X

Understand

In this paper we continue the study of the superconformal index of four-dimensional $\mathcal{N}=2$ theories of class $\mathcal{S}$ in the presence of surface defects.

Our main result is the construction of an algebra of difference operators, whose elements are labeled by irreducible representations of $A_{N-1}$.
For the fully antisymmetric tensor representations these difference operators are the Hamiltonians of the elliptic Ruijsenaars-Schneider system.
The structure constants of the algebra are elliptic generalizations of the Littlewood-Richardson coefficients.

Built on

G. Felder and A. Varchenko, Elliptic quantum groups and ruijsenaars models
1996
Earlier work this paper cites.
N. A. Nekrasov, Seiberg-Witten prepotential from instanton counting
2004
Earlier work this paper cites.
V. Fateev and A. Litvinov, On differential equation on four-point correlation function in the Conformal Toda Field Theory
2005
Earlier work this paper cites.
A. Kapustin, Wilson-’t Hooft operators in four-dimensional gauge theories and S-duality
2006
Earlier work this paper cites.
J. Kinney, J. M. Maldacena, S. Minwalla, and S. Raju, An Index for 4 dimensional super conformal theories
2007
Earlier work this paper cites.
V. Fateev and A. Litvinov, Correlation functions in conformal Toda field theory. I
Original
2007
Earlier work this paper cites.
N. Wyllard, A(N-1) conformal Toda field theory correlation functions from conformal N = 2 SU(N) quiver gauge theories
Original
2009
Earlier work this paper cites.
D. Gaiotto and E. Witten, Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory
Original
2009
Earlier work this paper cites.
D. Gaiotto and E. Witten, S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory
Original
2009
Earlier work this paper cites.
L. F. Alday and Y. Tachikawa, Affine SL(2) conformal blocks from 4d gauge theories
Original
2010
Earlier work this paper cites.
L. F. Alday, D. Gaiotto, and Y. Tachikawa, Liouville Correlation Functions from Four-dimensional Gauge Theories
Original
2010
Earlier work this paper cites.
L. F. Alday, D. Gaiotto, S. Gukov, Y. Tachikawa, and H. Verlinde, Loop and surface operators in N=2 gauge theory and Liouville modular geometry
Original
2010
Earlier work this paper cites.
A. Gadde, E. Pomoni, L. Rastelli, and S. S. Razamat, S-duality and 2d Topological QFT
Original
2010
Earlier work this paper cites.
A. Gadde, L. Rastelli, S. S. Razamat, and W. Yan, The Superconformal Index of the E6 SCFT
Original
2010
Earlier work this paper cites.
F. Benini, Y. Tachikawa, and D. Xie, Mirrors of 3d Sicilian theories
Original
2010
Earlier work this paper cites.

Similar

N. Drukker, J. Gomis, T. Okuda, and J. Teschner, Gauge Theory Loop Operators and Liouville Theory
Original
2010
Cited alongside, same era.
K. Hosomichi, S. Lee, and J. Park, AGT on the S-duality Wall
Original
2010
Cited alongside, same era.
D. Gaiotto and E. Witten, Janus Configurations, Chern-Simons Couplings, And The theta-Angle in N=4 Super Yang-Mills Theory
Original
2010
Cited alongside, same era.
L. Hadasz, Z. Jaskolski, and P. Suchanek, Modular bootstrap in Liouville field theory
Original
2010
Cited alongside, same era.
H. Kanno and Y. Tachikawa, Instanton counting with a surface operator and the chain-saw quiver
Original

Then

D. Gaiotto, N=2 dualities
Original
2012
Later among the works it cites.
D. Gaiotto and S. S. Razamat, Exceptional Indices
Original
2012
Later among the works it cites.
D. Gaiotto, Surface Operators in N = 2 4d Gauge Theories
Original
2012
Later among the works it cites.
A. Gadde and W. Yan, Reducing the 4d Index to the S 3 S^{3} Partition Function
Original
2012
Later among the works it cites.
J. Gomis, T. Okuda, and V. Pestun, Exact Results for ’t Hooft Loops in Gauge Theories on S 4 S^{4}
Original
2012
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

2011

Cited alongside, same era.

A. Gadde, L. Rastelli, S. S. Razamat, and W. Yan, The 4d Superconformal Index from q-deformed 2d Yang-Mills

2011

Cited alongside, same era.

T. Dimofte, S. Gukov, and L. Hollands, Vortex Counting and Lagrangian 3-manifolds

2011

Cited alongside, same era.

F. Dolan, V. Spiridonov, and G. Vartanov, From 4d superconformal indices to 3d partition functions

2011

Cited alongside, same era.

Y. Imamura, Relation between the 4d superconformal index and the S3 partition function

2011

Cited alongside, same era.

N. Drukker, D. Gaiotto, and J. Gomis, The Virtue of Defects in 4D Gauge Theories and 2D CFTs

2011

Cited alongside, same era.

J. Gomis and B. Le Floch, ’t Hooft Operators in Gauge Theory from Toda CFT

2011

Cited alongside, same era.

T. Nishioka, Y. Tachikawa, and M. Yamazaki, 3d Partition Function as Overlap of Wavefunctions

2011

Cited alongside, same era.

S. Benvenuti and S. Pasquetti, 3D-partition functions on the sphere: exact evaluation and mirror symmetry

2012

Later among the works it cites.

N. Hama and K. Hosomichi, Seiberg-Witten Theories on Ellipsoids

2012

Later among the works it cites.

V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops

2012

Later among the works it cites.

T. Okuda and V. Pestun, On the instantons and the hypermultiplet mass of N=2* super Yang-Mills on S 4 S^{4}

2012

Later among the works it cites.

A. Gadde, L. Rastelli, S. S. Razamat, and W. Yan, Gauge Theories and Macdonald Polynomials

2013

Later among the works it cites.

L. F. Alday, M. Bullimore, M. Fluder, and L. Hollands, Surface defects, the superconformal index and q-deformed Yang-Mills

Original

2013

Later among the works it cites.

D. Gaiotto, S. Gukov, and N. Seiberg, Surface Defects and Resolvents

2013

Later among the works it cites.

N. Doroud, J. Gomis, B. Le Floch, and S. Lee, Exact Results in D=2 Supersymmetric Gauge Theories

2013

Later among the works it cites.

A. Kapustin, B. Willett, and I. Yaakov, Exact results for supersymmetric abelian vortex loops in 2+1 dimensions

2013

Later among the works it cites.