Abstract
It was recently suggested that certain UV-completable supersymmetric actions can be characterized by the solutions to an auxiliary non-linear sigma-model with special asymptotic boundary conditions. The space-time of this sigma-model is the scalar field space of these effective theories while the target space is a coset space. We study this sigma-model without any reference to a potentially underlying geometric description. Using a holographic approach reminiscent of the bulk reconstruction in the AdS/CFT correspondence, we then derive its near-boundary solutions for a two-dimensional space-time. Specifying a set of Sl(2, ℝ) boundary data we show that the near-boundary solutions are uniquely fixed after imposing a single bulk-boundary matching condition. The reconstruction exploits an elaborate set of recursion relations introduced by Cattani, Kaplan, and Schmid in the proof of the Sl(2)-orbit theorem. We explicitly solve these recursion relations for three sets of simple boundary data and show that they model asymptotic periods of a Calabi-Yau threefold near the conifold point, the large complex structure point, and the Tyurin degeneration.
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References
E. Palti, The Swampland: Introduction and Review, Fortsch. Phys. 67 (2019) 1900037 [arXiv:1903.06239] [INSPIRE].
M. van Beest, J. Calderón-Infante, D. Mirfendereski and I. Valenzuela, Lectures on the Swampland Program in String Compactifications, arXiv:2102.01111 [INSPIRE].
H. Ooguri and C. Vafa, On the Geometry of the String Landscape and the Swampland, Nucl. Phys. B 766 (2007) 21 [hep-th/0605264] [INSPIRE].
D. Klaewer and E. Palti, Super-Planckian Spatial Field Variations and Quantum Gravity, JHEP 01 (2017) 088 [arXiv:1610.00010] [INSPIRE].
T.W. Grimm, E. Palti and I. Valenzuela, Infinite Distances in Field Space and Massless Towers of States, JHEP 08 (2018) 143 [arXiv:1802.08264] [INSPIRE].
B. Heidenreich, M. Reece and T. Rudelius, Emergence of Weak Coupling at Large Distance in Quantum Gravity, Phys. Rev. Lett. 121 (2018) 051601 [arXiv:1802.08698] [INSPIRE].
S.-J. Lee, W. Lerche and T. Weigand, Emergent strings from infinite distance limits, JHEP 02 (2022) 190 [arXiv:1910.01135] [INSPIRE].
S. Lanza, F. Marchesano, L. Martucci and I. Valenzuela, Swampland Conjectures for Strings and Membranes, JHEP 02 (2021) 006 [arXiv:2006.15154] [INSPIRE].
J. Calderón-Infante, A.M. Uranga and I. Valenzuela, The Convex Hull Swampland Distance Conjecture and Bounds on Non-geodesics, JHEP 03 (2021) 299 [arXiv:2012.00034] [INSPIRE].
S. Ashok and M.R. Douglas, Counting flux vacua, JHEP 01 (2004) 060 [hep-th/0307049] [INSPIRE].
B.S. Acharya and M.R. Douglas, A Finite landscape?, hep-th/0606212 [INSPIRE].
T.W. Grimm, Moduli space holography and the finiteness of flux vacua, JHEP 10 (2021) 153 [arXiv:2010.15838] [INSPIRE].
S. Cecotti, Special Geometry and the Swampland, JHEP 09 (2020) 147 [arXiv:2004.06929] [INSPIRE].
S. Cecotti, Moduli spaces of Calabi-Yau d-folds as gravitational-chiral instantons, JHEP 12 (2020) 008 [arXiv:2007.09992] [INSPIRE].
T.W. Grimm, C. Li and I. Valenzuela, Asymptotic Flux Compactifications and the Swampland, JHEP 06 (2020) 009 [Erratum ibid. 01 (2021) 007] [arXiv:1910.09549] [INSPIRE].
T.W. Grimm, C. Li and E. Palti, Infinite Distance Networks in Field Space and Charge Orbits, JHEP 03 (2019) 016 [arXiv:1811.02571] [INSPIRE].
P. Corvilain, T.W. Grimm and I. Valenzuela, The Swampland Distance Conjecture for Kähler moduli, JHEP 08 (2019) 075 [arXiv:1812.07548] [INSPIRE].
A. Font, A. Herráez and L.E. Ibáñez, The Swampland Distance Conjecture and Towers of Tensionless Branes, JHEP 08 (2019) 044 [arXiv:1904.05379] [INSPIRE].
T.W. Grimm and D. Van De Heisteeg, Infinite Distances and the Axion Weak Gravity Conjecture, JHEP 03 (2020) 020 [arXiv:1905.00901] [INSPIRE].
N. Gendler and I. Valenzuela, Merging the weak gravity and distance conjectures using BPS extremal black holes, JHEP 01 (2021) 176 [arXiv:2004.10768] [INSPIRE].
B. Bastian, T.W. Grimm and D. van de Heisteeg, Weak gravity bounds in asymptotic string compactifications, JHEP 06 (2021) 162 [arXiv:2011.08854] [INSPIRE].
T.W. Grimm and C. Li, Universal axion backreaction in flux compactifications, JHEP 06 (2021) 067 [arXiv:2012.08272] [INSPIRE].
S. Cecotti, Swampland geometry and the gauge couplings, JHEP 09 (2021) 136 [arXiv:2102.03205] [INSPIRE].
C. Robles, Classification of horizontal SL(2)s, Compositio Math. 152 (2016) 918 [arXiv:1405.3163].
M. Kerr, G. J. Pearlstein and C. Robles, Polarized relations on horizontal SL(2)’s, Doc. Math. 24 (2019) 1295.
W. Schmid, Variation of Hodge structure: the singularities of the period mapping, Invent. Math. 22 (1973) 211.
E. Cattani, A. Kaplan and W. Schmid, Degeneration of Hodge Structures, Ann. Math. 123 (1986) 457.
D. Harlow, TASI Lectures on the Emergence of Bulk Physics in AdS/CFT, PoS TASI2017 (2018) 002 [arXiv:1802.01040] [INSPIRE].
A. Hamilton, D.N. Kabat, G. Lifschytz and D.A. Lowe, Holographic representation of local bulk operators, Phys. Rev. D 74 (2006) 066009 [hep-th/0606141] [INSPIRE].
Y. Nakayama and H. Ooguri, Bulk Locality and Boundary Creating Operators, JHEP 10 (2015) 114 [arXiv:1507.04130] [INSPIRE].
M. Beccaria, H. Jiang and A.A. Tseytlin, Boundary correlators in WZW model on AdS2, JHEP 05 (2020) 099 [arXiv:2001.11269] [INSPIRE].
Y. Nakayama and Y. Nomura, Weak gravity conjecture in the AdS/CFT correspondence, Phys. Rev. D 92 (2015) 126006 [arXiv:1509.01647] [INSPIRE].
D. Harlow, Wormholes, Emergent Gauge Fields, and the Weak Gravity Conjecture, JHEP 01 (2016) 122 [arXiv:1510.07911] [INSPIRE].
N. Benjamin, E. Dyer, A.L. Fitzpatrick and S. Kachru, Universal Bounds on Charged States in 2d CFT and 3d Gravity, JHEP 08 (2016) 041 [arXiv:1603.09745] [INSPIRE].
M. Montero, G. Shiu and P. Soler, The Weak Gravity Conjecture in three dimensions, JHEP 10 (2016) 159 [arXiv:1606.08438] [INSPIRE].
M. Montero, Are tiny gauge couplings out of the Swampland?, JHEP 10 (2017) 208 [arXiv:1708.02249] [INSPIRE].
D. Harlow and H. Ooguri, Symmetries in quantum field theory and quantum gravity, Commun. Math. Phys. 383 (2021) 1669 [arXiv:1810.05338] [INSPIRE].
D. Harlow and H. Ooguri, Constraints on Symmetries from Holography, Phys. Rev. Lett. 122 (2019) 191601 [arXiv:1810.05337] [INSPIRE].
J.-B. Bae, S. Lee and J. Song, Modular Constraints on Superconformal Field Theories, JHEP 01 (2019) 209 [arXiv:1811.00976] [INSPIRE].
J.P. Conlon and F. Quevedo, Putting the Boot into the Swampland, JHEP 03 (2019) 005 [arXiv:1811.06276] [INSPIRE].
M. Montero, A Holographic Derivation of the Weak Gravity Conjecture, JHEP 03 (2019) 157 [arXiv:1812.03978] [INSPIRE].
Y.-H. Lin and S.-H. Shao, Anomalies and Bounds on Charged Operators, Phys. Rev. D 100 (2019) 025013 [arXiv:1904.04833] [INSPIRE].
J.P. Conlon and F. Revello, Moduli Stabilisation and the Holographic Swampland, LHEP 2020 (2020) 171 [arXiv:2006.01021] [INSPIRE].
H. Ooguri and T. Takayanagi, Cobordism Conjecture in AdS, arXiv:2006.13953 [INSPIRE].
F. Baume and J. Calderón Infante, Tackling the SDC in AdS with CFTs, JHEP 08 (2021) 057 [arXiv:2011.03583] [INSPIRE].
E. Perlmutter, L. Rastelli, C. Vafa and I. Valenzuela, A CFT distance conjecture, JHEP 10 (2021) 070 [arXiv:2011.10040] [INSPIRE].
S.K. Donaldson, Nahm’s equations and the classification of monopoles, Commun. Math. Phys. 96 (1984) 387 [INSPIRE].
A. Borel and J.-P. Serre, Corners and Arithmetic Groups, Commentarii mathematici Helvetici 48 (1973) 436.
T.W. Grimm, F. Ruehle and D. van de Heisteeg, Classifying Calabi–Yau Threefolds Using Infinite Distance Limits, Commun. Math. Phys. 382 (2021) 239 [arXiv:1910.02963] [INSPIRE].
G. Pearlstein, SL2-orbits and degenerations of mixed hodge structure, J. Diff. Geom. 74 (2006) 1.
A.N. Tyurin, Fano versus Calabi-Yau, The Fano Conference (2004) 701 [math/0302101].
A. Joshi and A. Klemm, Swampland Distance Conjecture for One-Parameter Calabi-Yau Threefolds, JHEP 08 (2019) 086 [arXiv:1903.00596] [INSPIRE].
P. Candelas, X.C. De La Ossa, P.S. Green and L. Parkes, A Pair of Calabi-Yau manifolds as an exactly soluble superconformal theory, Nucl. Phys. B 359 (1991) 21 [INSPIRE].
R. Blumenhagen, D. Kläwer, L. Schlechter and F. Wolf, The Refined Swampland Distance Conjecture in Calabi-Yau Moduli Spaces, JHEP 06 (2018) 052 [arXiv:1803.04989] [INSPIRE].
M. Demirtas, M. Kim, L. Mcallister and J. Moritz, Vacua with Small Flux Superpotential, Phys. Rev. Lett. 124 (2020) 211603 [arXiv:1912.10047] [INSPIRE].
M. Demirtas, M. Kim, L. McAllister and J. Moritz, Conifold Vacua with Small Flux Superpotential, Fortsch. Phys. 68 (2020) 2000085 [arXiv:2009.03312] [INSPIRE].
R. Álvarez-García, R. Blumenhagen, M. Brinkmann and L. Schlechter, Small Flux Superpotentials for Type IIB Flux Vacua Close to a Conifold, Fortsch. Phys. 68 (2020) 2000088 [arXiv:2009.03325] [INSPIRE].
B. Bastian, T.W. Grimm and D. van de Heisteeg, Modeling General Asymptotic Calabi-Yau Periods, arXiv:2105.02232 [INSPIRE].
T.W. Grimm and J. Monnee, Deformed WZW Models and Hodge Theory — Part I, arXiv:2112.00031 [INSPIRE].
C. Teitelboim, Gravitation and Hamiltonian Structure in Two Space-Time Dimensions, Phys. Lett. B 126 (1983) 41 [INSPIRE].
R. Jackiw, Lower Dimensional Gravity, Nucl. Phys. B 252 (1985) 343 [INSPIRE].
S.-J. Lee, W. Lerche and T. Weigand, Tensionless Strings and the Weak Gravity Conjecture, JHEP 10 (2018) 164 [arXiv:1808.05958] [INSPIRE].
S.-J. Lee, W. Lerche and T. Weigand, A Stringy Test of the Scalar Weak Gravity Conjecture, Nucl. Phys. B 938 (2019) 321 [arXiv:1810.05169] [INSPIRE].
F. Marchesano and M. Wiesner, Instantons and infinite distances, JHEP 08 (2019) 088 [arXiv:1904.04848] [INSPIRE].
S.-J. Lee, W. Lerche and T. Weigand, Emergent strings, duality and weak coupling limits for two-form fields, JHEP 02 (2022) 096 [arXiv:1904.06344] [INSPIRE].
F. Baume, F. Marchesano and M. Wiesner, Instanton Corrections and Emergent Strings, JHEP 04 (2020) 174 [arXiv:1912.02218] [INSPIRE].
D. Klaewer, S.-J. Lee, T. Weigand and M. Wiesner, Quantum corrections in 4d N = 1 infinite distance limits and the weak gravity conjecture, JHEP 03 (2021) 252 [arXiv:2011.00024] [INSPIRE].
S. Lanza, F. Marchesano, L. Martucci and I. Valenzuela, The EFT stringy viewpoint on large distances, JHEP 09 (2021) 197 [arXiv:2104.05726] [INSPIRE].
R. Hain, Periods of Limit Mixed Hodge Structures, Current Develop. Math. 2002 (2003) 113, [math/0305090].
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Grimm, T.W., Monnee, J. & van de Heisteeg, D. Bulk reconstruction in moduli space holography. J. High Energ. Phys. 2022, 10 (2022). https://doi.org/10.1007/JHEP05(2022)010
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DOI: https://doi.org/10.1007/JHEP05(2022)010