Miura operators, degenerate fields and the M2-M5 intersection

We determine the mathematical structures which govern the Ω deformation of supersymmetric intersections of M2 and M5 branes. We find that the supersymmetric intersections govern many aspects of the theory of W-algebras, including degenerate modules, the Miura transform and Coulomb gas constructions. We give an algebraic interpretation of the Pandharipande-Thomas box counting in ℂ 3 .

[1]  Tomáš Procházka,et al.  Webs of W-algebras , 2017, Journal of High Energy Physics.

[2]  D. Gaiotto,et al.  Prepared for submission to JHEP Aspects of Ω-deformed M-theory , 2019 .

[3]  Richard P. Thomas,et al.  The 3-fold vertex via stable pairs , 2007, 0709.3823.

[4]  Clay Córdova,et al.  Surface defects and chiral algebras , 2017, 1704.01955.

[5]  H. Nakajima,et al.  Quantized Coulomb branches of Jordan quiver gauge theories and cyclotomic rational Cherednik algebras , 2016, Proceedings of Symposia in Pure Mathematics.

[6]  E. Witten,et al.  The omega deformation, branes, integrability and Liouville theory , 2010, 1002.0888.

[7]  Quiver Yangian and Supersymmetric Quantum Mechanics , 2020, 2008.07006.

[8]  B. Estienne,et al.  Relating Jack wavefunctions to theories , 2009, 0906.1969.

[9]  E. Witten,et al.  Knot Invariants from Four-Dimensional Gauge Theory , 2011, 1106.4789.

[10]  C. Peng,et al.  Twin-plane-partitions and N$$ \mathcal{N} $$ = 2 affine Yangian , 2018, Journal of High Energy Physics.

[11]  String theory dynamics in various dimensions , 1995, hep-th/9503124.

[12]  T. Creutzig,et al.  Vertex Algebras for S-duality , 2017, Communications in Mathematical Physics.

[13]  K. Brown.  Symplectic Reflection Algebras , 2003, Irish Mathematical Society Bulletin.

[14]  P. Alam.  ‘L’ , 2021, Composites Engineering: An A–Z Guide.

[15]  K. Costello.  Holography and Koszul duality: the example of the $M2$ brane , 2017, 1705.02500.

[16]  Junya Yagi.  Compactification on the Ω-background and the AGT correspondence , 2012, 1205.6820.

[17]  L. Rastelli,et al.  N=4 superconformal bootstrap. , 2013, Physical review letters.

[18]  O. Schiffmann,et al.  Cherednik algebras, W-algebras and the equivariant cohomology of the moduli space of instantons on A2 , 2012, Publications mathématiques de l'IHÉS.

[19]  K. Costello.  M-theory in the Omega-background and 5-dimensional non-commutative gauge theory , 2016, 1610.04144.

[20]  Yaping Yang,et al.  On deformed double current algebras for simple Lie algebras , 2016, 1608.02900.

[21]  Tomáš Procházka.  W$$ \mathcal{W} $$ -symmetry, topological vertex and affine Yangian , 2015, 1512.07178.

[22]  B. Bernevig,et al.  Electron-quasihole duality and second-order differential equation for Read-Rezayi and Jack wave functions , 2010, 1005.3475.

[23]  C. Beem,et al.  Secondary Products in Supersymmetric Field Theory , 2018, Annales Henri Poincaré.

[24]  D. Gaiotto,et al.  Vertex algebras at the corner , 2017, Journal of High Energy Physics.

[25]  S. Pufu,et al.  Solving M-theory with the conformal bootstrap , 2017, Journal of High Energy Physics.

[26]  Elaine Savory.  Boundaries , 2012 .

[27]  S. Pufu,et al.  The M-theory S-matrix from ABJM: beyond 11D supergravity , 2018, Journal of High Energy Physics.

[28]  Helen Jenne,et al.  Combinatorics of the double-dimer model , 2019, Advances in Mathematics.

[29]  Victor Ginzburg,et al.  Symplectic reflection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism , 2000 .

[30]  K. Costello,et al.  Quantization of open-closed BCOV theory, I , 2015, 1505.06703.

[31]  B. Feigin,et al.  Plane partitions with a “pit”: generating functions and representation theory , 2015, 1512.08779.

[32]  Tomáš Procházka,et al.  W$$ \mathcal{W} $$ -algebra modules, free fields, and Gukov-Witten defects , 2018, Journal of High Energy Physics.

[33]  D. Gaiotto,et al.  Boundary Chiral Algebras and Holomorphic Twists , 2020, Communications in Mathematical Physics.

[34]  E. Witten,et al.  Algebra of the Infrared: String Field Theoretic Structures in Massive ${\cal N}=(2,2)$ Field Theory In Two Dimensions , 2015, 1506.04087.

[35]  Junya Yagi.  Ω-deformation and quantization , 2014, 1405.6714.

[36]  I. Gordon,et al.  Symplectic reflection algebras , 2007, 0712.1568.

[37]  P. Alam.  ‘S’ , 2021, Composites Engineering: An A–Z Guide.

[38]  D. Gaiotto,et al.  Twisted M2 brane holography and sphere correlation functions , 2020, 2004.13810.

[39]  L. Alday,et al.  6d (2, 0) and M-theory at 1-loop , 2020, Journal of High Energy Physics.

[40]  L. Rastelli,et al.  The (2, 0) superconformal bootstrap , 2015, 1507.05637.

[41]  N. Guay.  Affine Yangians and deformed double current algebras in type A , 2007 .

[42]  Y. Soibelman,et al.  Cohomological Hall Algebras, Vertex Algebras and Instantons , 2018, Communications in Mathematical Physics.

[43]  V. Fateev,et al.  The Models of Two-Dimensional Conformal Quantum Field Theory with Z(n) Symmetry , 1988 .

[44]  V. V. Sokolov,et al.  Lie algebras and equations of Korteweg-de Vries type , 1985 .

[45]  P. Vanhove,et al.  Duality and higher derivative terms in M theory , 2005, hep-th/0510027.

[46]  A. Litvinov,et al.  On W algebras commuting with a set of screenings , 2016, 1609.06271.

[47]  Y. Soibelman,et al.  Cohomological Hall algebras and perverse coherent sheaves on toric Calabi-Yau 3-folds. , 2020, 2007.13365.

[48]  Koichira Harada,et al.  Plane partition realization of (web of) W$$ \mathcal{W} $$-algebra minimal models , 2018, Journal of High Energy Physics.

[49]  A. Linshaw.  Universal two-parameter $\mathcal{W}_{\infty}$-algebra and vertex algebras of type $\mathcal{W}(2,3,\dots, N)$ , 2017, 1710.02275.

[50]  C. Peng,et al.  The supersymmetric affine Yangian , 2017, 1711.07449.

[51]  E. Witten,et al.  Eleven-dimensional supergravity on a manifold with boundary , 1996, hep-th/9603142.

[52]  Tomáš Procházka.  Exploring W∞$$ {\mathcal{W}}_{\infty } $$ in the quadratic basis , 2014, 1411.7697.

[53]  A. Tsymbaliuk.  The affine Yangian of gl1 revisited , 2014, 1404.5240.

[54]  B. Estienne,et al.  Conformal blocks in Virasoro and W theories: duality and the Calogero-Sutherland model , 2011, 1110.1101.

[55]  N. Guay.  Cherednik algebras and Yangians , 2005 .

[56]  R. Gopakumar,et al.  Higher spins and Yangian symmetries , 2017, 1702.05100.

[57]  R. Gopakumar,et al.  Triality in minimal model holography , 2012, 1205.2472.

[58]  Tom'avs Proch'azka.  Instanton R-matrix and $$ \mathcal{W} $$-symmetry , 2019, 1903.10372.

[59]  J. Cardy,et al.  Calogero–Sutherland model and bulk-boundary correlations in conformal field theory , 2003, hep-th/0310291.

[60]  E. Opdam.  Lecture notes on Dunkl operators for real and complex reflection groups , 2000 .