Abstract
We describe progress in using the field theory of tensionless strings to arrive at a Lagrangian for the six-dimensional \( \mathcal{N}=\left(2,0\right) \) conformal theory. We construct the free part of the theory and propose an ansatz for the cubic vertex in light-cone superspace. By requiring closure of the (2, 0) supersymmetry algebra, we fix the cubic vertex up to two parameters.
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W. Nahm, Supersymmetries and their representations, Nucl. Phys. B 135 (1978) 149 [INSPIRE].
E. Witten, Some comments on string dynamics, in Future perspectives in string theory. Proceedings, Conference, Strings’95, Los Angeles, U.S.A., 13–18 March 1995, pg. 501 [hep-th/9507121] [INSPIRE].
A. Strominger, Open p-branes, Phys. Lett. B 383 (1996) 44 [hep-th/9512059] [INSPIRE].
G.W. Moore, Lecture notes for Felix Klein lectures, http://www.physics.rutgers.edu/~gmoore/FelixKleinLectureNotes.pdf, (2012).
K.G. Wilson and J.B. Kogut, The renormalization group and the ϵ-expansion, Phys. Rept. 12 (1974) 75 [INSPIRE].
A.M. Polyakov, Conformal symmetry of critical fluctuations, JETP Lett. 12 (1970) 381 [Pisma Zh. Eksp. Teor. Fiz. 12 (1970) 538] [INSPIRE].
O. Aharony, M. Berkooz, S. Kachru, N. Seiberg and E. Silverstein, Matrix description of interacting theories in six-dimensions, Adv. Theor. Math. Phys. 1 (1998) 148 [hep-th/9707079] [INSPIRE].
O. Aharony, M. Berkooz and N. Seiberg, Light cone description of (2, 0) superconformal theories in six-dimensions, Adv. Theor. Math. Phys. 2 (1998) 119 [hep-th/9712117] [INSPIRE].
N. Arkani-Hamed, A.G. Cohen, D.B. Kaplan, A. Karch and L. Motl, Deconstructing (2, 0) and little string theories, JHEP 01 (2003) 083 [hep-th/0110146] [INSPIRE].
M.R. Douglas, On D = 5 super Yang-Mills theory and (2, 0) theory, JHEP 02 (2011) 011 [arXiv:1012.2880] [INSPIRE].
N. Lambert, C. Papageorgakis and M. Schmidt-Sommerfeld, M5-branes, D4-branes and quantum 5D super-Yang-Mills, JHEP 01 (2011) 083 [arXiv:1012.2882] [INSPIRE].
P.-M. Ho, K.-W. Huang and Y. Matsuo, A non-Abelian self-dual gauge theory in 5 + 1 dimensions, JHEP 07 (2011) 021 [arXiv:1104.4040] [INSPIRE].
K.-W. Huang, R. Roiban and A.A. Tseytlin, Self-dual 6d 2-form fields coupled to non-Abelian gauge field: quantum corrections, JHEP 06 (2018) 134 [arXiv:1804.05059] [INSPIRE].
H. Samtleben, E. Sezgin and R. Wimmer, (1, 0) superconformal models in six dimensions, JHEP 12 (2011) 062 [arXiv:1108.4060] [INSPIRE].
C.-S. Chu and S.-L. Ko, Non-Abelian action for multiple five-branes with self-dual tensors, JHEP 05 (2012) 028 [arXiv:1203.4224] [INSPIRE].
F. Bonetti, T.W. Grimm and S. Hohenegger, Non-Abelian tensor towers and (2, 0) superconformal theories, JHEP 05 (2013) 129 [arXiv:1209.3017] [INSPIRE].
C. Sämann and L. Schmidt, Towards an M5-brane model I: a 6d superconformal field theory, J. Math. Phys. 59 (2018) 043502 [arXiv:1712.06623] [INSPIRE].
C. Beem, M. Lemos, L. Rastelli and B.C. van Rees, The (2, 0) superconformal bootstrap, Phys. Rev. D 93 (2016) 025016 [arXiv:1507.05637] [INSPIRE].
S. Kovacs, Y. Sato and H. Shimada, Membranes from monopole operators in ABJM theory: large angular momentum and M-theoretic AdS 4 /CFT 3, PTEP 2014 (2014) 093B01 [arXiv:1310.0016] [INSPIRE].
S. Kovacs, Y. Sato and H. Shimada, On membrane interactions and a three-dimensional analog of Riemann surfaces, JHEP 02 (2016) 050 [arXiv:1508.03367] [INSPIRE].
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].
D.E. Berenstein, J.M. Maldacena and H.S. Nastase, Strings in flat space and pp waves from N = 4 super Yang-Mills, JHEP 04 (2002) 013 [hep-th/0202021] [INSPIRE].
S. Mandelstam, Light cone superspace and the ultraviolet finiteness of the N = 4 model, Nucl. Phys. B 213 (1983) 149 [INSPIRE].
A.K.H. Bengtsson, I. Bengtsson and L. Brink, Cubic interaction terms for arbitrarily extended supermultiplets, Nucl. Phys. B 227 (1983) 41 [INSPIRE].
A. Sagnotti, Notes on strings and higher spins, J. Phys. A 46 (2013) 214006 [arXiv:1112.4285] [INSPIRE].
E. Witten, Noncommutative geometry and string field theory, Nucl. Phys. B 268 (1986) 253 [INSPIRE].
G. Bonelli, On the tensionless limit of bosonic strings, infinite symmetries and higher spins, Nucl. Phys. B 669 (2003) 159 [hep-th/0305155] [INSPIRE].
A. Schild, Classical null strings, Phys. Rev. D 16 (1977) 1722 [INSPIRE].
F. Lizzi, B. Rai, G. Sparano and A. Srivastava, Quantization of the null string and absence of critical dimensions, Phys. Lett. B 182 (1986) 326 [INSPIRE].
A. Karlhede and U. Lindström, The classical bosonic string in the zero tension limit, Class. Quant. Grav. 3 (1986) L73 [INSPIRE].
U. Lindström, B. Sundborg and G. Theodoridis, The zero tension limit of the superstring, Phys. Lett. B 253 (1991) 319 [INSPIRE].
U. Lindström, B. Sundborg and G. Theodoridis, The zero tension limit of the spinning string, Phys. Lett. B 258 (1991) 331 [INSPIRE].
J. Isberg, U. Lindström and B. Sundborg, Space-time symmetries of quantized tensionless strings, Phys. Lett. B 293 (1992) 321 [hep-th/9207005] [INSPIRE].
J. Isberg, U. Lindström, B. Sundborg and G. Theodoridis, Classical and quantized tensionless strings, Nucl. Phys. B 411 (1994) 122 [hep-th/9307108] [INSPIRE].
H. Gustafsson, U. Lindström, P. Saltsidis, B. Sundborg and R. van Unge, Hamiltonian BRST quantization of the conformal string, Nucl. Phys. B 440 (1995) 495 [hep-th/9410143] [INSPIRE].
R. Amorim and J. Barcelos-Neto, Strings with zero tension, Z. Phys. C 38 (1988) 643 [INSPIRE].
J. Gamboa, C. Ramirez and M. Ruiz-Altaba, Quantum null (super)strings, Phys. Lett. B 225 (1989) 335 [INSPIRE].
J. Gamboa, C. Ramirez and M. Ruiz-Altaba, Null spinning strings, Nucl. Phys. B 338 (1990) 143 [INSPIRE].
J. Barcelos-Neto and M. Ruiz-Altaba, Superstrings with zero tension, Phys. Lett. B 228 (1989) 193 [INSPIRE].
A. Bagchi, S. Chakrabortty and P. Parekh, Tensionless superstrings: view from the worldsheet, JHEP 10 (2016) 113 [arXiv:1606.09628] [INSPIRE].
A.K.H. Bengtsson, I. Bengtsson and L. Brink, Cubic interaction terms for arbitrary spin, Nucl. Phys. B 227 (1983) 31 [INSPIRE].
Y.S. Akshay and S. Ananth, Fermi-Bose cubic couplings in light-cone field theories, Phys. Rev. D 91 (2015) 085029 [arXiv:1504.00967] [INSPIRE].
S. Ananth, Deriving field theories for particles of arbitrary spin with and without supersymmetry, in Proceedings, International Workshop on Higher Spin Gauge Theories, Singapore, 4–6 November 2015, World Scientific, Singapore, (2017), pg. 255 [arXiv:1603.02795] [INSPIRE].
S. Ananth, A. Kar, S. Majumdar and N. Shah, Deriving spin-1 quartic interaction vertices from closure of the Poincaré algebra, Nucl. Phys. B 926 (2018) 11 [arXiv:1707.05871] [INSPIRE].
L. Brink, O. Lindgren and B.E.W. Nilsson, N = 4 Yang-Mills theory on the light cone, Nucl. Phys. B 212 (1983) 401 [INSPIRE].
S. Ananth, L. Brink, S.-S. Kim and P. Ramond, Non-linear realization of PSU(2, 2|4) on the light-cone, Nucl. Phys. B 722 (2005) 166 [hep-th/0505234] [INSPIRE].
M.B. Green and J.H. Schwarz, Superstring interactions, Nucl. Phys. B 218 (1983) 43 [INSPIRE].
M.B. Green, J.H. Schwarz and L. Brink, Superfield theory of type II superstrings, Nucl. Phys. B 219 (1983) 437 [INSPIRE].
M.B. Green and J.H. Schwarz, The structure of superstring field theories, Phys. Lett. B 140 (1984) 33 [INSPIRE].
M.B. Green and J.H. Schwarz, Superstring field theory, Nucl. Phys. B 243 (1984) 475 [INSPIRE].
N. Linden, Lorentz generators in light cone gauge superstring field theory, Nucl. Phys. B 286 (1987) 429 [INSPIRE].
S. Mandelstam, Interacting string picture of dual resonance models, Nucl. Phys. B 64 (1973) 205 [INSPIRE].
S. Mandelstam, Lorentz properties of the three-string vertex, Nucl. Phys. B 83 (1974) 413 [INSPIRE].
M. Kaku and K. Kikkawa, The field theory of relativistic strings, 1. Trees, Phys. Rev. D 10 (1974) 1110 [INSPIRE].
M. Kaku and K. Kikkawa, The field theory of relativistic strings. 2. Loops and pomerons, Phys. Rev. D 10 (1974) 1823 [INSPIRE].
E. Cremmer and J.-L. Gervais, Combining and splitting relativistic strings, Nucl. Phys. B 76 (1974) 209 [INSPIRE].
E. Cremmer and J.-L. Gervais, Infinite component field theory of interacting relativistic strings and dual theory, Nucl. Phys. B 90 (1975) 410 [INSPIRE].
C. Marshall and P. Ramond, Field theory of the interacting string: the closed string, Nucl. Phys. B 85 (1975) 375 [INSPIRE].
A.K.H. Bengtsson and N. Linden, Interacting covariant open bosonic strings from the light cone J i−, Phys. Lett. B 187 (1987) 289 [INSPIRE].
T. Kugo, Lorentz transformation in the light cone gauge string field theory, Prog. Theor. Phys. 78 (1987) 690 [INSPIRE].
S.-J. Sin, Lorentz invariance of light cone string field theories, Nucl. Phys. B 306 (1988) 282 [INSPIRE].
Y. Saitoh and Y. Tanii, Lorentz symmetry in the light cone field theory of open and closed strings, Nucl. Phys. B 325 (1989) 161 [INSPIRE].
Y. Saitoh and Y. Tanii, Quantum Lorentz covariance in the light cone string field theory, Nucl. Phys. B 331 (1990) 744 [INSPIRE].
K. Kikkawa and S. Sawada, Cancellation of Lorentz anomaly of the string field theory in light cone gauge, Nucl. Phys. B 335 (1990) 677 [INSPIRE].
P. Ramond, private communication, unpublished.
S. Ananth, L. Brink and P. Ramond, unpublished.
P.S. Howe, G. Sierra and P.K. Townsend, Supersymmetry in six-dimensions, Nucl. Phys. B 221 (1983) 331 [INSPIRE].
J.A. Strathdee, Extended Poincaré supersymmetry, Int. J. Mod. Phys. A 2 (1987) 273 [INSPIRE].
P. Goddard, J. Goldstone, C. Rebbi and C.B. Thorn, Quantum dynamics of a massless relativistic string, Nucl. Phys. B 56 (1973) 109 [INSPIRE].
L. Brink, O. Lindgren and B.E.W. Nilsson, The ultraviolet finiteness of the N = 4 Yang-Mills theory, Phys. Lett. B 123 (1983) 323 [INSPIRE].
P. Claus, R. Kallosh and A. Van Proeyen, M5-brane and superconformal (0, 2) tensor multiplet in six-dimensions, Nucl. Phys. B 518 (1998) 117 [hep-th/9711161] [INSPIRE].
R. Giles and C.B. Thorn, A lattice approach to string theory, Phys. Rev. D 16 (1977) 366 [INSPIRE].
C.B. Thorn, Reformulating string theory with the 1/N expansion, in The First International A.D. Sakharov Conference on Physics, Moscow, U.S.S.R., 27–31 May 1991, pg. 447 [hep-th/9405069] [INSPIRE].
Yu. M. Makeenko and A.A. Migdal, Exact equation for the loop average in multicolor QCD, Phys. Lett. B 88 (1979) 135 [Erratum ibid. B 89 (1980) 437] [INSPIRE].
Yu. Makeenko and A.A. Migdal, Quantum chromodynamics as dynamics of loops, Nucl. Phys. B 188 (1981) 269 [Sov. J. Nucl. Phys. 32 (1980) 431] [Yad. Fiz. 32 (1980) 838] [INSPIRE].
A.A. Migdal, Loop equations and 1/N expansion, Phys. Rept. 102 (1983) 199 [INSPIRE].
N. Drukker, D.J. Gross and H. Ooguri, Wilson loops and minimal surfaces, Phys. Rev. D 60 (1999) 125006 [hep-th/9904191] [INSPIRE].
N. Drukker, A new type of loop equations, JHEP 11 (1999) 006 [hep-th/9908113] [INSPIRE].
A.M. Polyakov and V.S. Rychkov, Gauge field strings duality and the loop equation, Nucl. Phys. B 581 (2000) 116 [hep-th/0002106] [INSPIRE].
A.M. Polyakov and V.S. Rychkov, Loop dynamics and AdS/CFT correspondence, Nucl. Phys. B 594 (2001) 272 [hep-th/0005173] [INSPIRE].
G.W. Semenoff and D. Young, Wavy Wilson line and AdS/CFT, Int. J. Mod. Phys. A 20 (2005) 2833 [hep-th/0405288] [INSPIRE].
H. Hata and A. Miwa, Loop equation in D = 4, N = 4 SYM and string field equation on AdS 5 × S5, Phys. Rev. D 73 (2006) 046001 [hep-th/0510150] [INSPIRE].
J. Polchinski and J. Sully, Wilson loop renormalization group flows, JHEP 10 (2011) 059 [arXiv:1104.5077] [INSPIRE].
H. Kunitomo and S. Mizoguchi, Lorentz anomaly in the semi-light-cone gauge superstrings, Prog. Theor. Phys. 118 (2007) 559 [arXiv:0706.3982] [INSPIRE].
W. Taylor, D-brane field theory on compact spaces, Phys. Lett. B 394 (1997) 283 [hep-th/9611042] [INSPIRE].
N. Seiberg, New theories in six-dimensions and matrix description of M-theory on T 5 and T 5/Z 2, Phys. Lett. B 408 (1997) 98 [hep-th/9705221] [INSPIRE].
O. Aharony, A brief review of ‘little string theories’, Class. Quant. Grav. 17 (2000) 929 [hep-th/9911147] [INSPIRE].
M.B. Green and N. Seiberg, Contact interactions in superstring theory, Nucl. Phys. B 299 (1988) 559 [INSPIRE].
J. Greensite and F.R. Klinkhamer, New interactions for superstrings, Nucl. Phys. B 281 (1987) 269 [INSPIRE].
J. Greensite and F.R. Klinkhamer, Contact interactions in closed superstring field theory, Nucl. Phys. B 291 (1987) 557 [INSPIRE].
J. Greensite and F.R. Klinkhamer, Superstring amplitudes and contact interactions, Nucl. Phys. B 304 (1988) 108 [INSPIRE].
B. de Wit, J. Hoppe and H. Nicolai, On the quantum mechanics of supermembranes, Nucl. Phys. B 305 (1988) 545 [INSPIRE].
T. Banks, W. Fischler, S.H. Shenker and L. Susskind, M theory as a matrix model: a conjecture, Phys. Rev. D 55 (1997) 5112 [hep-th/9610043] [INSPIRE].
J. Goldstone, unpublished, (1982).
J. Hoppe, Quantum theory of a massless relativistic surface and a two-dimensional bound state problem, Ph.D. thesis, M.I.T., U.S.A., (1982).
A.A. Belavin, A.M. Polyakov and A.B. Zamolodchikov, Infinite conformal symmetry in two-dimensional quantum field theory, Nucl. Phys. B 241 (1984) 333 [INSPIRE].
D. Friedan, E.J. Martinec and S.H. Shenker, Conformal invariance, supersymmetry and string theory, Nucl. Phys. B 271 (1986) 93 [INSPIRE].
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Ananth, S., Kovacs, S., Sato, Y. et al. Towards a tensionless string field theory for the \( \mathcal{N}=\left(2,0\right) \) CFT in d = 6. J. High Energ. Phys. 2018, 135 (2018). https://doi.org/10.1007/JHEP07(2018)135
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DOI: https://doi.org/10.1007/JHEP07(2018)135