Geodesic
Surface Defects in E-String Compactifications and the van Diejen Model
Symmetry, integrability and geometry: methods and applications, Tome 14 (2018) Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study the supersymmetric index of four dimensional theories obtained by compactifications of the six dimensional E string theory on a Riemann surface. In particular we derive the difference operator introducing certain class of surface defects to the index computation. The difference operator turns out to be, up to a constant shift, an analytic difference operator discussed by van Diejen.
Keywords: QFT; supersymmetry; analytic difference operators. 
@article{SIGMA_2018_14_a35,
     author = {Belal Nazzal and Shlomo S. Razamat},
     title = {Surface {Defects} in {E-String} {Compactifications} and the van {Diejen} {Model}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2018},
     volume = {14},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a35/}
}
TY  - JOUR
AU  - Belal Nazzal
AU  - Shlomo S. Razamat
TI  - Surface Defects in E-String Compactifications and the van Diejen Model
JO  - Symmetry, integrability and geometry: methods and applications
PY  - 2018
VL  - 14
UR  - http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a35/
LA  - en
ID  - SIGMA_2018_14_a35
ER  - 
%0 Journal Article
%A Belal Nazzal
%A Shlomo S. Razamat
%T Surface Defects in E-String Compactifications and the van Diejen Model
%J Symmetry, integrability and geometry: methods and applications
%D 2018
%V 14
%U http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a35/
%G en
%F SIGMA_2018_14_a35
Belal Nazzal; Shlomo S. Razamat. Surface Defects in E-String Compactifications and the van Diejen Model. Symmetry, integrability and geometry: methods and applications, Tome 14 (2018). http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a35/

[1] Alday L. F., Gaiotto D., Tachikawa Y., “Liouville correlation functions from four-dimensional gauge theories”, Lett. Math. Phys., 91 (2010), 167–197, arXiv: 0906.3219 | DOI | MR

[2] Arthamonov S., Shakirov S., Genus two generalization of $A_1$ spherical DAHA, arXiv: 1704.02947

[3] Bhardwaj L., “Classification of 6d ${\mathcal N}=(1,0)$ gauge theories”, J. High Energy Phys., 2015:11 (2015), 002, 26 pp., arXiv: 1502.06594 | DOI | MR

[4] Del Zotto M., Heckman J. J., Tomasiello A., Vafa C., “6d conformal matter”, J. High Energy Phys., 2015:2 (2015), 054, 56 pp., arXiv: 1407.6359 | DOI | MR

[5] Derkachev S.É., Spiridonov V. P., “The Yang–Baxter equation, parameter permutations, and the elliptic beta integral”, Russian Math. Surveys, 68 (2013), 1027–1072, arXiv: 1205.3520 | DOI | MR

[6] van Diejen J. F., “Integrability of difference Calogero–Moser systems”, J. Math. Phys., 35 (1994), 2983–3004 | DOI | MR

[7] Dolan F. A., Osborn H., “Applications of the superconformal index for protected operators and $q$-hypergeometric identities to ${\mathcal N}=1$ dual theories”, Nuclear Phys. B, 818 (2009), 137–178, arXiv: 0801.4947 | DOI | MR

[8] Gadde A., Pomoni E., Rastelli L., Razamat S. S., “$S$-duality and 2d topological QFT”, J. High Energy Phys., 2010:3 (2010), 032, 22 pp., arXiv: 0910.2225 | DOI | MR

[9] Gadde A., Rastelli L., Razamat S. S., Yan W., “Gauge theories and Macdonald polynomials”, Comm. Math. Phys., 319 (2013), 147–193, arXiv: 1110.3740 | DOI | MR

[10] Gaiotto D., Rastelli L., Razamat S. S., “Bootstrapping the superconformal index with surface defects”, J. High Energy Phys., 2013:1 (2013), 022, 54 pp., arXiv: 1207.3577 | DOI | MR

[11] Gaiotto D., Razamat S. S., “${\mathcal N}=1$ theories of class ${\mathcal S}_k$”, J. High Energy Phys., 2015:7 (2015), 073, 64 pp., arXiv: 1503.05159 | DOI | MR

[12] Gaiotto D., Tomasiello A., “Holography for $(1,0)$ theories in six dimensions”, J. High Energy Phys., 2014:12 (2014), 003, 28 pp., arXiv: 1404.0711 | DOI | MR

[13] Gorsky A., Nekrasov N., “Hamiltonian systems of Calogero-type, and two-dimensional Yang–Mills theory”, Nuclear Phys. B, 414 (1994), 213–238, arXiv: hep-th/9304047 | DOI | MR

[14] Heckman J. J., Morrison D. R., Rudelius T., Vafa C., “Atomic classification of 6D SCFTs”, Fortschr. Phys., 63 (2015), 468–530, arXiv: 1502.05405 | DOI

[15] Heckman J. J., Morrison D. R., Vafa C., “On the classification of 6D SCFTs and generalized ADE orbifolds”, J. High Energy Phys., 2014:5 (2014), 028, 49 pp. ; Erratum, J. High Energy Phys., 2015:6 (2015), 017, 2 pp., arXiv: 1312.5746 | DOI | DOI

[16] Intriligator K., Pouliot P., “Exact superpotentials, quantum vacua and duality in supersymmetric ${\rm Sp}(N_c)$ gauge theories”, Phys. Lett. B, 353 (1995), 471–476, arXiv: hep-th/9505006 | DOI | MR

[17] Ito Y., Yoshida Y., Superconformal index with surface defects for class ${\mathcal S}_k$, arXiv: 1606.01653

[18] Kim H. C., Razamat S. S., Vafa C., Zafrir G., “E-string rheory on Riemann surfaces”, Fortschr. Phys., 66 (2018), 1700074, 35 pp., arXiv: 1709.02496 | DOI | MR

[19] Kinney J., Maldacena J., Minwalla S., Raju S., “An index for 4 dimensional super conformal theories”, Comm. Math. Phys., 275 (2007), 209–254, arXiv: hep-th/0510251 | DOI | MR

[20] Koornwinder T. H., “Askey–Wilson polynomials for root systems of type $BC$”, Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications (Tampa, FL, 1991), Contemp. Math., 138, Amer. Math. Soc., Providence, RI, 1992, 189–204 | DOI | MR

[21] Maruyoshi K., Yagi J., “Surface defects as transfer matrices”, Prog. Theor. Exp. Phys., 2016 (2016), 113B01, 52 pp., arXiv: 1606.01041 | DOI | MR

[22] Morrison D. R., Taylor W., “Classifying bases for 6D F-theory models”, Cent. Eur. J. Phys., 10 (2012), 1072–1088, arXiv: 1201.1943

[23] Nekrasov N., “BPS/CFT correspondence: non-perturbative Dyson–Schwinger equations and $qq$-characters”, J. High Energy Phys., 2016:3 (2016), 181, 70 pp., arXiv: 1512.05388 | DOI | MR

[24] Nekrasov N. A., Shatashvili S. L., “Quantization of integrable systems and four dimensional gauge theories”, XVIth International Congress on Mathematical Physics, World Sci. Publ., Hackensack, NJ, 2010, 265–289, arXiv: 0908.4052 | DOI | MR

[25] Rains E., Ruijsenaars S., “Difference operators of Sklyanin and van Diejen type”, Comm. Math. Phys., 320 (2013), 851–889, arXiv: 1203.0042 | DOI | MR

[26] Rains E. M., “Transformations of elliptic hypergeometric integrals”, Ann. of Math., 171 (2010), 169–243, arXiv: math.QA/0309252 | DOI | MR

[27] Ruijsenaars S. N. M., “Hilbert–Schmidt operators vs. integrable systems of elliptic Calogero–Moser type IV. The relativistic Heun (van Diejen) case”, SIGMA, 11 (2015), 004, 78 pp., arXiv: 1404.4392 | MR

[28] Spiridonov V. P., Elliptic hypergeometric functions, A complement to the book by G.E. Andrews, R. Askey, R. Roy, Special functions, Encyclopedia of Math. Appl. Vol. 71, Cambridge University Press, Cambridge, 1999, written for its Russian edition: Moscow, MCCME, 2013, pp. 577–606, arXiv: 0704.3099

[29] Spiridonov V. P., “On the elliptic beta function”, Russian Math. Surveys, 56 (2001), 185–186 | DOI | MR

[30] Spiridonov V. P., Warnaar S. O., “Inversions of integral operators and elliptic beta integrals on root systems”, Adv. Math., 207 (2006), 91–132, arXiv: math.CA/0411044 | DOI | MR

[31] Yagi J., “Surface defects and elliptic quantum groups”, J. High Energy Phys., 2017:6 (2017), 013, 32 pp., arXiv: 1701.05562 | DOI | MR

[32] Yamazaki M., “New integrable models from the gauge/YBE correspondence”, J. Stat. Phys., 154 (2014), 895–911, arXiv: 1307.1128 | DOI | MR