Abstract
We study restrictions on scattering amplitudes on the worldvolume of branes and strings (such as confining flux tubes in QCD) implied by the target space Poincaré symmetry. We focus on exploring the conditions for the string worldsheet theory to be integrable. We prove that for a higher dimensional membrane the scattering amplitudes for the translational Goldstone modes (“branons”) are double soft. At one-loop double softness is generically violated for the string worldsheet scattering as a consequence of collinear singularities. Violation of double softness implies in turn the breakdown of integrability. We prove that if branons are the only gapless degrees of freedom then the worldsheet integrability is compatible with target space Poincaré symmetry only if the number of space-time dimensions is equal to D = 26 (a critical bosonic string), and for D = 3. We extend the analysis to include massless worldsheet fermions, resulting from spontaneous breakdown of the target space supersymmetry. We check that the tree-level integrability in this case is in one-to-one correspondence with the existence of a -symmetric Green-Schwarz (GS) action. As a byproduct we show that at the leading order in the derivative expansion an \( \mathcal{N}=1 \) superstring without -symmetry in D = 3, 4, 6, 10 dimensions exhibits an accidental enhanced supersymmetry and is equivalent to a -symmetric \( \mathcal{N}=2 \) GS superstring.
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References
G. Veneziano, Construction of a crossing-symmetric, Regge behaved amplitude for linearly rising trajectories, Nuovo Cim. A 57 (1968) 190 [INSPIRE].
M. Shifman and A. Vainshtein, Highly Excited Mesons, Linear Regge Trajectories and the Pattern of the Chiral Symmetry Realization, Phys. Rev. D 77 (2008) 034002 [arXiv:0710.0863] [INSPIRE].
N. Beisert et al., Review of AdS/CFT Integrability: An Overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].
N. Gromov, V. Kazakov, S. Leurent and D. Volin, Quantum spectral curve for arbitrary state/operator in AdS 5 /CFT 4, arXiv:1405.4857 [INSPIRE].
S. Dubovsky, R. Flauger and V. Gorbenko, Evidence from Lattice Data for a New Particle on the Worldsheet of the QCD Flux Tube, Phys. Rev. Lett. 111 (2013) 062006 [arXiv:1301.2325] [INSPIRE].
S. Dubovsky, R. Flauger and V. Gorbenko, Flux Tube Spectra from Approximate Integrability at Low Energies, J. Exp. Theor. Phys. 120 (2015) 399 [arXiv:1404.0037] [INSPIRE].
A. Athenodorou, B. Bringoltz and M. Teper, Closed flux tubes and their string description in D=3 + 1 SU(N) gauge theories, JHEP 02 (2011) 030 [arXiv:1007.4720] [INSPIRE].
A. Athenodorou and M. Teper, Closed flux tubes in higher representations and their string description in D = 2 + 1 SU(N) gauge theories, JHEP 06 (2013) 053 [arXiv:1303.5946] [INSPIRE].
S. Dubovsky, R. Flauger and V. Gorbenko, Effective String Theory Revisited, JHEP 09 (2012) 044 [arXiv:1203.1054] [INSPIRE].
M.B. Green and J.H. Schwarz, Covariant Description of Superstrings, Phys. Lett. B 136 (1984) 367 [INSPIRE].
W. Siegel, Hidden Local Supersymmetry in the Supersymmetric Particle Action, Phys. Lett. B 128 (1983) 397 [INSPIRE].
L. Mezincescu, A.J. Routh and P.K. Townsend, All Superparticles are BPS, J. Phys. A 47 (2014) 175401 [arXiv:1401.5116] [INSPIRE].
C.G. Callan Jr., S.R. Coleman, J. Wess and B. Zumino, Structure of phenomenological Lagrangians. 2., Phys. Rev. 177 (1969) 2247 [INSPIRE].
C.J. Isham, A. Salam and J.A. Strathdee, Nonlinear realizations of space-time symmetries. Scalar and tensor gravity, Annals Phys. 62 (1971) 98 [INSPIRE].
D.V. Volkov, Phenomenological Lagrangians, Fiz. Elem. Chast. Atom. Yadra 4 (1973) 3.
E. Ivanov and V. Ogievetsky, The Inverse Higgs Phenomenon in Nonlinear Realizations, Teor. Mat. Fiz. 25 (1975) 164.
M. Bando, T. Kugo and K. Yamawaki, Nonlinear Realization and Hidden Local Symmetries, Phys. Rept. 164 (1988) 217 [INSPIRE].
N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the Simplest Quantum Field Theory?, JHEP 09 (2010) 016 [arXiv:0808.1446] [INSPIRE].
D. Kapec, V. Lysov, S. Pasterski and A. Strominger, Semiclassical Virasoro symmetry of the quantum gravity S-matrix, JHEP 08 (2014) 058 [arXiv:1406.3312] [INSPIRE].
S. Dubovsky, R. Flauger and V. Gorbenko, Solving the Simplest Theory of Quantum Gravity, JHEP 09 (2012) 133 [arXiv:1205.6805] [INSPIRE].
J. Polchinski and A. Strominger, Effective string theory, Phys. Rev. Lett. 67 (1991) 1681 [INSPIRE].
P. Dorey, Exact S matrices, hep-th/9810026 [INSPIRE].
A.B. Zamolodchikov and A.B. Zamolodchikov, Factorized s Matrices in Two-Dimensions as the Exact Solutions of Certain Relativistic Quantum Field Models, Annals Phys. 120 (1979) 253 [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. Mezincescu and P.K. Townsend, Anyons from Strings, Phys. Rev. Lett. 105 (2010) 191601 [arXiv:1008.2334] [INSPIRE].
S.R. Coleman, There are no Goldstone bosons in two-dimensions, Commun. Math. Phys. 31 (1973) 259.
S. Weinberg, Current-commutator theory of multiple pion production, Phys. Rev. Lett. 16 (1966) 879.
S.R. Coleman and H. Thun, On the Prosaic Origin of the Double Poles in the Sine-Gordon S Matrix, Commun. Math. Phys. 61 (1978) 31.
J. Hughes and J. Polchinski, Partially Broken Global Supersymmetry and the Superstring, Nucl. Phys. B 278 (1986) 147 [INSPIRE].
E. Ivanov and S. Krivonos, N = 1 D = 4 supermembrane in the coset approach, Phys. Lett. B 453 (1999) 237 [hep-th/9901003] [INSPIRE].
D.V. Volkov and V.P. Akulov, Possible universal neutrino interaction, JETP Lett. 16 (1972) 438 [INSPIRE].
D.V. Volkov and V.P. Akulov, Is the Neutrino a Goldstone Particle?, Phys. Lett. B 46 (1973) 109 [INSPIRE].
J.M. Rabin, Supermanifold Cohomology and the Wess-Zumino Term of the Covariant Superstring Action, Commun. Math. Phys. 108 (1987) 375.
M. Henneaux and L. Mezincescu, A σ-model Interpretation of Green-Schwarz Covariant Superstring Action, Phys. Lett. B 152 (1985) 340 [INSPIRE].
J. Wess and B. Zumino, Consequences of anomalous Ward identities, Phys. Lett. B 37 (1971) 95 [INSPIRE].
L. Mezincescu, A.J. Routh and P.K. Townsend, Equivalence of 3D Spinning String and Superstring, JHEP 07 (2013) 024 [arXiv:1305.5049] [INSPIRE].
A.R. Kavalov and A.G. Sedrakyan, Quantum geometry of the covariant superstring with N = 1 global supersymmetry, Phys. Lett. B 182 (1986) 33.
W. Siegel, Light Cone Analysis of Covariant Superstring, Nucl. Phys. B 236 (1984) 311 [INSPIRE].
L. Mezincescu and P.K. Townsend, Quantum 3D Superstrings, Phys. Rev. D 84 (2011) 106006 [arXiv:1106.1374] [INSPIRE].
Z. Bern, L.J. Dixon and D.A. Kosower, Dimensionally regulated pentagon integrals, Nucl. Phys. B 412 (1994) 751 [hep-ph/9306240] [INSPIRE].
L.U. Ancarani and G. Gasaneo, Derivatives of any order of the Gaussian hypergeometric function 2 F 1(a, b, c; z) with respect to the parameters a, b and c, J. Phys. A 42 (2009) 395208 [INSPIRE].
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ArXiv ePrint: 1411.0703
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Cooper, P., Dubovsky, S., Gorbenko, V. et al. Looking for integrability on the worldsheet of confining strings. J. High Energ. Phys. 2015, 127 (2015). https://doi.org/10.1007/JHEP04(2015)127
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DOI: https://doi.org/10.1007/JHEP04(2015)127