Abstract
Recently, a worldsheet dual to free \( \mathcal{N} \) = 4 Super Yang-Mills has been proposed in terms of twistor variables for AdS5, in parallel to that for the AdS3 dual to the free symmetric orbifold CFT. In the latter case, holomorphic covering maps play a central role in determining correlators and are associated to Feynman diagrams. After recasting these maps in terms of the worldsheet twistor variables for AdS3, we generalise to AdS5. We propose stringy incidence relations and appropriate reality conditions for the twistor covering maps. For some special kinematic configurations of correlators, we exhibit an explicit construction of the corresponding covering map. We find that the closed string worldsheet corresponding to this map is related to a gauge theory Feynman diagram by the Strebel construction, as for AdS3/CFT2. Rather strikingly, the regularised Strebel area of the worldsheet reproduces the Feynman propagator of the free field theory.
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References
M.R. Gaberdiel and R. Gopakumar, String Dual to Free N = 4 Supersymmetric Yang-Mills Theory, Phys. Rev. Lett. 127 (2021) 131601 [arXiv:2104.08263] [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, The worldsheet dual of free super Yang-Mills in 4D, JHEP 11 (2021) 129 [arXiv:2105.10496] [INSPIRE].
N. Berkovits, A New Limit of the AdS5 × S5 Sigma Model, JHEP 08 (2007) 011 [hep-th/0703282] [INSPIRE].
N. Berkovits and C. Vafa, Towards a Worldsheet Derivation of the Maldacena Conjecture, JHEP 03 (2008) 031 [arXiv:0711.1799] [INSPIRE].
N. Berkovits, Perturbative Super-Yang-Mills from the Topological AdS5 × S5 Sigma Model, JHEP 09 (2008) 088 [arXiv:0806.1960] [INSPIRE].
N. Berkovits, Sketching a Proof of the Maldacena Conjecture at Small Radius, JHEP 06 (2019) 111 [arXiv:1903.08264] [INSPIRE].
L. Eberhardt, M.R. Gaberdiel and R. Gopakumar, The Worldsheet Dual of the Symmetric Product CFT, JHEP 04 (2019) 103 [arXiv:1812.01007] [INSPIRE].
L. Eberhardt, M.R. Gaberdiel and R. Gopakumar, Deriving the AdS3/CFT2 correspondence, JHEP 02 (2020) 136 [arXiv:1911.00378] [INSPIRE].
L. Eberhardt, AdS3/CFT2 at higher genus, JHEP 05 (2020) 150 [arXiv:2002.11729] [INSPIRE].
A. Dei, M.R. Gaberdiel, R. Gopakumar and B. Knighton, Free field world-sheet correlators for AdS3, JHEP 02 (2021) 081 [arXiv:2009.11306] [INSPIRE].
M.R. Gaberdiel, R. Gopakumar, B. Knighton and P. Maity, From symmetric product CFTs to AdS3, JHEP 05 (2021) 073 [arXiv:2011.10038] [INSPIRE].
B. Knighton, Higher genus correlators for tensionless AdS3 strings, JHEP 04 (2021) 211 [arXiv:2012.01445] [INSPIRE].
M.R. Gaberdiel, B. Knighton and J. Vošmera, D-branes in AdS3 × S3 × 𝕋4 at k = 1 and their holographic duals, JHEP 12 (2021) 149 [arXiv:2110.05509] [INSPIRE].
M.R. Gaberdiel, R. Gopakumar and C. Hull, Stringy AdS3 from the worldsheet, JHEP 07 (2017) 090 [arXiv:1704.08665] [INSPIRE].
K. Ferreira, M.R. Gaberdiel and J.I. Jottar, Higher spins on AdS3 from the worldsheet, JHEP 07 (2017) 131 [arXiv:1704.08667] [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, Tensionless string spectra on AdS3, JHEP 05 (2018) 085 [arXiv:1803.04423] [INSPIRE].
G. Giribet, C. Hull, M. Kleban, M. Porrati and E. Rabinovici, Superstrings on AdS3 at k = 1, JHEP 08 (2018) 204 [arXiv:1803.04420] [INSPIRE].
A. Giveon, D. Kutasov, E. Rabinovici and A. Sever, Phases of quantum gravity in AdS3 and linear dilaton backgrounds, Nucl. Phys. B 719 (2005) 3 [hep-th/0503121] [INSPIRE].
B. Balthazar, A. Giveon, D. Kutasov and E.J. Martinec, Asymptotically free AdS3/CFT2, JHEP 01 (2022) 008 [arXiv:2109.00065] [INSPIRE].
E.J. Martinec, AdS3’s with and without BTZ’s, arXiv:2109.11716 [INSPIRE].
L. Eberhardt, A perturbative CFT dual for pure NS-NS AdS3 strings, J. Phys. A 55 (2022) 064001 [arXiv:2110.07535] [INSPIRE].
D.E. Berenstein, J.M. Maldacena and H.S. Nastase, Strings in flat space and pp waves from N = 4 superYang-Mills, JHEP 04 (2002) 013 [hep-th/0202021] [INSPIRE].
N. Berkovits, An Alternative string theory in twistor space for N = 4 superYang-Mills, Phys. Rev. Lett. 93 (2004) 011601 [hep-th/0402045] [INSPIRE].
L. Mason and D. Skinner, Ambitwistor strings and the scattering equations, JHEP 07 (2014) 048 [arXiv:1311.2564] [INSPIRE].
E. Witten, Perturbative gauge theory as a string theory in twistor space, Commun. Math. Phys. 252 (2004) 189 [hep-th/0312171] [INSPIRE].
C. Ahn, Worldsheet free fields, higher spin symmetry, and free N = 4 super-Yang-Mills theory, Phys. Rev. D 105 (2022) 066006 [arXiv:2109.09260] [INSPIRE].
O. Lunin and S.D. Mathur, Correlation functions for MN/SN orbifolds, Commun. Math. Phys. 219 (2001) 399 [hep-th/0006196] [INSPIRE].
A. Pakman, L. Rastelli and S.S. Razamat, Diagrams for Symmetric Product Orbifolds, JHEP 10 (2009) 034 [arXiv:0905.3448] [INSPIRE].
R. Gopakumar, From free fields to AdS, Phys. Rev. D 70 (2004) 025009 [hep-th/0308184] [INSPIRE].
R. Gopakumar, From free fields to AdS. 2, Phys. Rev. D 70 (2004) 025010 [hep-th/0402063] [INSPIRE].
R. Gopakumar, From free fields to AdS: III, Phys. Rev. D 72 (2005) 066008 [hep-th/0504229] [INSPIRE].
K. Strebel, Quadratic Differentials, Springer, Berlin, Heidelberg, Germany (1984) [DOI].
M. Mulase and M. Penkava, Ribbon Graphs, Quadratic Differentials on Riemann Surfaces, and Algebraic Curves Defined over \( \overline{\mathbb{Q}} \), Asian J. Math. 2 (1998) 875 [math-ph/9811024].
S.S. Razamat, On a worldsheet dual of the Gaussian matrix model, JHEP 07 (2008) 026 [arXiv:0803.2681] [INSPIRE].
R. Gopakumar, What is the Simplest Gauge-String Duality?, arXiv:1104.2386 [INSPIRE].
R. Gopakumar and R. Pius, Correlators in the Simplest Gauge-String Duality, JHEP 03 (2013) 175 [arXiv:1212.1236] [INSPIRE].
T. Adamo, D. Skinner and J. Williams, Twistor methods for AdS5, JHEP 08 (2016) 167 [arXiv:1607.03763] [INSPIRE].
T. Adamo, Lectures on twistor theory, PoS Modave2017 (2018) 003 [arXiv:1712.02196] [INSPIRE].
M.R. Gaberdiel, R. Gopakumar, B. Knighton and P. Maity, work in progress.
B. Eynard, Lectures on Compact Riemann Surfaces, [arXiv:1805.06405].
K. Roumpedakis, Comments on the SN orbifold CFT in the large N-limit, JHEP 07 (2018) 038 [arXiv:1804.03207] [INSPIRE].
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ArXiv ePrint: 2112.05115
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Bhat, F., Gopakumar, R., Maity, P. et al. Twistor coverings and Feynman diagrams. J. High Energ. Phys. 2022, 150 (2022). https://doi.org/10.1007/JHEP05(2022)150
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DOI: https://doi.org/10.1007/JHEP05(2022)150