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2017

Line defect Schur indices, Verlinde algebras and $U(1)_r$ fixed points

Neitzke, Andrew, Yan, Fei

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Given an $\mathcal{N}=2$ superconformal field theory, we reconsider the Schur index $\mathcal{I}_L(q)$ in the presence of a half line defect $L$.

Recently Cordova-Gaiotto-Shao found that $\mathcal{I}_L(q)$ admits an expansion in terms of characters of the chiral algebra $\mathcal{A}$ introduced by Beem et al., with simple coefficients $v_{L,\beta}(q)$.
We report a puzzling new feature of this expansion: the $q \to 1$ limit of the coefficients $v_{L_,\beta}(q)$ is linearly related to the vacuum expectation values $\langle L \rangle$ in $U(1)_r$-invariant vacua of the theory compactified on $S^1$.
This relation can be expressed algebraically as a commutative diagram involving three algebras: the algebra generated by line defects, the algebra of functions on $U(1)_r$-invariant vacua, and a Verlinde-like algebra associated to $\mathcal{A}$.

Line defect Schur indices, Verlinde algebras and $U(1)_r$ fixed points · Around

Built on

N. J. Hitchin, “The self-duality equations on a Riemann surface,” Proc. London Math. Soc. (3)
1987
Earlier work this paper cites.
E. P. Verlinde, “Fusion Rules and Modular Transformations in 2D Conformal Field Theory,” Nucl. Phys
1988
Earlier work this paper cites.
V. G. Kac and M. Wakimoto, “Modular invariant representations of infinite-dimensional Lie algebras and superalgebras,” Proc. Nat. Acad. Sci. U.S.A
1988
Earlier work this paper cites.
I. Koh and P. Sorba, “Fusion rules and (sub)modular invariant partition functions in nonunitary theories,,” Phys. Letter. B
1988
Earlier work this paper cites.
P. C. Argyres and M. R. Douglas, “New phenomena in SU(3) supersymmetric gauge theory,” Nucl. Phys
1995
Earlier work this paper cites.
P. C. Argyres, M. R. Plesser, N. Seiberg, and E. Witten, “New N=2 superconformal field theories in four-dimensions,” Nucl. Phys
1996
Earlier work this paper cites.
K. De Vos and P. Van Driel, “The Kazhdan-Lusztig conjecture for W algebras,” J. Math. Phys
1996
Earlier work this paper cites.
Springer-Verlag, New York, 1997
P. Di Francesco, P. Mathieu, and D. Sénéchal, Conformal field theory · 1997
Earlier work this paper cites.
PhD thesis, Oxford University, 1998
T. Hausel, Geometry of the moduli space of Higgs bundles · 1998
Earlier work this paper cites.
M. R. Douglas, B. Fiol, and C. Romelsberger, “Stability and BPS branes,” JHEP
2005
Earlier work this paper cites.
M. R. Douglas, B. Fiol, and C. Romelsberger, “The Spectrum of BPS branes on a noncompact Calabi-Yau,” JHEP
2005
Earlier work this paper cites.
V. Fock and A. Goncharov, “Moduli spaces of local systems and higher Teichmüller theory,” Publ. Math. Inst. Hautes Études Sci
2006
Earlier work this paper cites.
J. Kinney, J. M. Maldacena, S. Minwalla, and S. Raju, “An Index for 4 dimensional super conformal theories,” Commun. Math. Phys
2007
Earlier work this paper cites.
N. Drukker, D. R. Morrison, and T. Okuda, “Loop operators and S-duality from curves on Riemann surfaces,” JHEP
Original
2009
Earlier work this paper cites.
D. Gaiotto, G. W. Moore, and A. Neitzke, “Four-dimensional wall-crossing via three-dimensional field theory,” Commun. Math. Phys
Original
2010
Earlier work this paper cites.
N. Drukker, J. Gomis, T. Okuda, and J. Teschner, “Gauge Theory Loop Operators and Liouville Theory,” JHEP
Original
2010
Earlier work this paper cites.

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