北京雁栖湖应用数学研究院

References or Resources:<ul><li><a href='https://arxiv.org/pdf/2212.06187' target='_blank'>https://arxiv.org/pdf/2212.06187</a></li><li><a href='https://arxiv.org/abs/2501.00966' target='_blank'>https://arxiv.org/abs/2501.00966</a></li><li><a href='https://arxiv.org/abs/2402.00981' target='_blank'>https://arxiv.org/abs/2402.00981</a></li></ul>

Main Reading:<ul><li>Intro and Section 4 of "Symmetries and Strings in Field Theory and Gravity," T. Banks and N. Seiberg, <a href="https://arxiv.org/abs/1011.5120" target="_blank">https://arxiv.org/abs/1011.5120</a></li><li>Chapter 0 of "The Kinematics of Quantum Gravity," J. M. (my dissertation), available at <a href="https://dash.lib.harvard.edu/handle/1/37372201" target="_blank">https://dash.lib.harvard.edu/handle/1/37372201</a></li></ul>Classic References:<ul><li>"Classical physics as geometry: Gravitation, electromagnetism, unquantized charge, and mass as properties of curved empty space," C. Misner, J. Wheeler, <a href="https://inspirehep.net/literature/42728" target="_blank">https://inspirehep.net/literature/42728</a></li><li>"Constraints on String Vacua with Space-Time Supersymmetry," T. Banks, L. Dixon, <a href="https://inspirehep.net/literature/260812" target="_blank">https://inspirehep.net/literature/260812</a></li><li>"Monopoles, Duality, and String Theory," J. Polchinski, <a href="https://arxiv.org/abs/hep-th/0304042" target="_blank">https://arxiv.org/abs/hep-th/0304042</a></li><li>"The String Landscape, Black Holes and Gravity as the Weakest Force," N. Arkani-Hamed, L. Motl, A. Nicolis, C. Vafa, <a href="https://arxiv.org/abs/hep-th/0601001" target="_blank">https://arxiv.org/abs/hep-th/0601001</a></li><li>"Symmetries and Strings in Field Theory and Gravity," T. Banks and N. Seiberg, <a href="https://arxiv.org/abs/1011.5120" target="_blank">https://arxiv.org/abs/1011.5120</a></li></ul>Unifying the Kinematic Swampland:<ul><li>"Cobordism Classes and the Swampland," J. M., C. Vafa, <a href="https://arxiv.org/abs/1909.10355" target="_blank">https://arxiv.org/abs/1909.10355</a></li><li>"Topological Operators and Completeness of Spectrum in Discrete Gauge Theories," T. Rudelius, S.-H. Shao, <a href="https://arxiv.org/abs/2006.10052" target="_blank">https://arxiv.org/abs/2006.10052</a></li><li>"Chern-Weil Global Symmetries and How Quantum Gravity Avoids Them," B. Heidenreich, J. M., M. Montero, M. Reece, T. Rudelius, I. Valenzuela, <a href="https://arxiv.org/abs/2012.00009" target="_blank">https://arxiv.org/abs/2012.00009</a></li><li>"Non-Invertible Global Symmetries and Completeness of the Spectrum," B. Heidenreich, J. M., M. Montero, M. Reece, T. Rudelius, I. Valenzuela, <a href="https://arxiv.org/abs/2104.07036" target="_blank">https://arxiv.org/abs/2104.07036</a></li><li>"Gravitational Solitons and Completeness," J. M., <a href="https://arxiv.org/abs/2108.02228" target="_blank">https://arxiv.org/abs/2108.02228</a></li></ul>Symmetries, Holography, and Factorization:<ul><li>"Wormholes, Emergent Gauge Fields, and the Weak Gravity Conjecture," D. Harlow, <a href="https://arxiv.org/abs/1510.07911" target="_blank">https://arxiv.org/abs/1510.07911</a></li><li>"Symmetries in quantum field theory and quantum gravity," D. Harlow, H. Ooguri, <a href="https://arxiv.org/abs/1810.05338" target="_blank">https://arxiv.org/abs/1810.05338</a></li><li>"Baby Universes, Holography, and the Swampland," J. M., C. Vafa, <a href="https://arxiv.org/abs/2004.06738" target="_blank">https://arxiv.org/abs/2004.06738</a></li></ul>

Reference<ul><li>W. Taylor, “TASI Lectures on Supergravity and String Vacua in Various Dimensions,” [arXiv:1104.2051 [hep-th]]. </li><li>J. de Boer, R. Dijkgraaf, K. Hori, A. Keurentjes, J. Morgan, D. R. Morrison and S. Sethi, Adv. Theor. Math. Phys. 4, 995-1186 (2002) doi:10.4310/ATMP.2000.v4.n5.a1 [arXiv:hep-th/0103170 [hep-th]]. </li><li>A. Bedroya, Y. Hamada, M. Montero and C. Vafa, “Compactness of brane moduli and the String Lamppost Principle in d > 6,” JHEP 02, 082 (2022) doi:10.1007/JHEP02(2022)082 [arXiv:2110.10157 [hep-th]].</li></ul>

References or Resources:<ul><li>R. Blumenhagen, D. Lüst, S. Theisen, “Basic Concepts of String Theory," Chapter 14.</li><li>M. Graña, "Flux compactifications in string theory: A Comprehensive review,” (mostly sections 5 and 6).</li></ul>

Moduli stabilization is one of the most interesting and important goals in string phenomenology. After lots of new constructions and ideas in the early 2000's we have entered a phase of careful checks and scrutiny. This led to swampland conjectures that call into question the existence of dS vacua as well as scale-separated AdS vacua in string theory. I will review the current status of well-known string compactification scenarios like KKLT, LVS and DGKT as well as other ideas to stabilize moduli in string compactifications. References or Resources: <href="https://arxiv.org/pdf/2310.20559" target="_blank">2310.20559</a> Chapters 1-5 and 9

Pedagogical introduction to orbifolds with concrete examples:<ul><li>R. Blumenhagen, D. Lüst and S. Theisen, Basic concepts of string theory. Theoretical and Mathematical Physics. Springer, Heidelberg, Germany, 2013.</li><li>Suggested reading: chapters 10, 11 and 15</li><li>Suggested focus on heteretotic/type II toroidal compactifications and orbifolds, being able to understand the lattice construction and points of symmetry enhancement e.g. page 277(chapter 10.2) and being able reproduce the spectrum of 15.2 orbifolds will provide a good introduction to the fundamentals. Also I will try to use the same notation so familiarity with those chapters will be very helpful.</li></ul>Geometric Orbifolds<ul><li>L. J. Dixon, J. A. Harvey, C. Vafa and E. Witten, Strings on Orbifolds, Nucl. Phys. B 261 (1985) 678–686</li><li>L. J. Dixon, J. A. Harvey, C. Vafa and E. Witten, Strings on Orbifolds. 2., Nucl. Phys. B 274 (1986) 285–314</li></ul>Non-geometric orbifolds:<ul><li>K. S. Narain, M. H. Sarmadi and C. Vafa, Asymmetric Orbifolds, Nucl. Phys. B 288 (1987) 551.</li><li>J. A. Harvey, G. W. Moore and C. Vafa, Quasicrystalline Compactification, Nucl. Phys. B 304 (1988) 269–290</li><li>A. Dabholkar and J. A. Harvey, String islands, JHEP 02 (1999) 006 [hep-th/9809122].</li><li>K. S. Narain, M. H. Sarmadi and C. Vafa, Asymmetric orbifolds: Path integral and operator formulations, Nucl. Phys. B 356 (1991) 163–207.</li><li>C. Vafa, Modular Invariance and Discrete Torsion on Orbifolds, Nucl. Phys. B 273 (1986) 592–606.</li><li>G. Gkountoumis, C. Hull, K. Stemerdink and S. Vandoren, Freely acting orbifolds of type IIB string theory on T5, JHEP 08 (2023) 089 [2302.09112].</li><li>Z. K. Baykara, Y. Hamada, H.-C. Tarazi and C. Vafa, On the String Landscape Without Hypermultiplets, 2309.15152.</li><li>Z. K. Baykara, H.-C. Tarazi and C. Vafa, The Quasicrystalline String Landscape, 2406.00129.</li></ul>Non-susy orbifolds:<ul><li>L. J. Dixon and J. A. Harvey, String Theories in Ten-Dimensions Without Space-Time Supersymmetry, Nucl. Phys. B 274 (1986) 93–105.</li><li>L. Alvarez-Gaume, P. H. Ginsparg, G. W. Moore and C. Vafa, An O(16) x O(16) Heterotic String, Phys. Lett. B 171 (1986) 155–162.</li><li>P. H. Ginsparg and C. Vafa, Toroidal Compactification of Nonsupersymmetric Heterotic Strings, Nucl. Phys. B 289 (1987) 414.</li><li>B. Fraiman, M. Graña, H. Parra De Freitas and S. Sethi, Non-Supersymmetric Heterotic Strings on a Circle, 2307.13745.</li><li>Z. K. Baykara, H.-C. Tarazi and C. Vafa, New Non-Susy Tachyon-Free Strings, 2406.00185.</li></ul>

Referece: <a href='https://link.springer.com/referenceworkentry/10.1007/978-981-19-3079-9_67-1' target='_blank'>https://link.springer.com/referenceworkentry/10.1007/978-981-19-3079-9_67-1</a>

Reference: <ul><li>Montero, Miguel, et al. "The dark dimension and the Swampland." Journal of High Energy Physics 2023.2 (2023): 1-18. <a href='https://arxiv.org/abs/2205.12293' target='_blank'>https://arxiv.org/abs/2205.12293</a></li><li>Obied, Georges, et al. "Dark dimension and decaying dark matter gravitons." Physical Review D 109.6 (2024): 063540. <a href='https://arxiv.org/abs/2209.09249' target='_blank'>https://arxiv.org/abs/2209.09249</a></li><li>Law-Smith, Jamie AP, et al. "Astrophysical constraints on decaying dark gravitons." Journal of High Energy Physics 2024.6 (2024): 1-26. <a href='https://arxiv.org/abs/2307.11048' target='_blank'>https://arxiv.org/abs/2307.11048</a></li><li>Gonzalo, Eduardo, et al. "Dark dimension gravitons as dark matter." Journal of High Energy Physics 2023.11 (2023): 1-18. <a href='https://arxiv.org/abs/2311.05318' target='_blank'>https://arxiv.org/abs/2311.05318</a></li></ul>

References or Resources:<ul><li><a href='https://arxiv.org/abs/hep-th/9602022' target='_blank'>https://arxiv.org/abs/hep-th/9602022</a></li><li><a href='https://arxiv.org/abs/hep-th/9602114' target='_blank'>https://arxiv.org/abs/hep-th/9602114</a></li><li><a href='https://arxiv.org/abs/hep-th/9603161' target='_blank'>https://arxiv.org/abs/hep-th/9603161</a></li><li><a href='https://arxiv.org/abs/1806.01854' target='_blank'>https://arxiv.org/abs/1806.01854</a></li><li><a href='https://arxiv.org/abs/2212.06187' target='_blank'>https://arxiv.org/abs/2212.06187</a></li><li><a href='https://arxiv.org/pdf/2201.03660' target='_blank'>https://arxiv.org/pdf/2201.03660</a></li><li><a href='https://arxiv.org/abs/1910.01135' target='_blank'>https://arxiv.org/abs/1910.01135</a></li><li><a href='https://arxiv.org/abs/1502.05405' target='_blank'>https://arxiv.org/abs/1502.05405</a></li><li><a href='https://arxiv.org/abs/1511.05565' target='_blank'>https://arxiv.org/abs/1511.05565</a></li><li><a href='https://arxiv.org/abs/2411.19155' target='_blank'>https://arxiv.org/abs/2411.19155</a></li><li><a href='https://arxiv.org/abs/1801.04036' target='_blank'>https://arxiv.org/abs/1801.04036</a></li></ul>

In this talk I discuss holographic constraints on scale separated, supersymmetric AdS vacua of IIB string theory and M-theory. Their dual CFTs should have very large central charges and rather unusual properties. I first describe brane configurations that source these would-be AdS flux compactifications. Subsequently, I identify certain UV AdS geometries in the near horizon limit of these branes. Lastly, I explain how to obtain bounds on the absolute values of the cosmological constants of the AdS vacua from the central charges of the dual CFTs.

In this talk, I will introduce a new scale called the black hole scale which marks the inverse length (or the temperature) of the smallest Schwarzschild black hole where the EFT of quantum gravity gives a correct description of its free energy. This new scale is motivated from Swampland principles and is hard to detect from the viewpoint of the EFT. In particular, the black hole scale gets related to the Gregory-Laflamme transition in the decompactification limit and to the Horowitz-Polchinski solutions in the light perturbative string limits. Then, motivated by the identification of the black hole scale in quantum gravity, I will discuss recent progress in finding higher-dimensional analogues of the Horowitz-Polchinski solutions.

In this talk I discuss holographic constraints on scale separated, supersymmetric AdS vacua of IIB string theory and M-theory. Their dual CFTs should have very large central charges and rather unusual properties. I first describe brane configurations that source these would-be AdS flux compactifications. Subsequently, I identify certain UV AdS geometries in the near horizon limit of these branes. Lastly, I explain how to obtain bounds on the absolute values of the cosmological constants of the AdS vacua from the central charges of the dual CFTs.

I will discuss non-geometric flux compactifications of string theory on Landau-Ginzburg models that are dual to rigid Calabi-Yau manifolds. Minkowski vacua can be analyzed even at strong coupling, providing a rare window in this corner of the string theory landscape. We focus on the number of stabilized moduli to test the tadpole conjecture in this context. While the conjecture is confirmed, a refined version is violated and needs to be modified. We furthermore discuss the existence of Minkowski vacua in which all scalar fields are stabilized. For some of these vacua all scalars fields are massive, while others have also some massless but stabilized scalar fields.

In this talk I will discuss concrete examples of string theory compactifications that are non-geometric. From the susy perspective such examples provide us with a more complete understanding of the string theory landscape that does not come from geometry. I will also discuss the importance of such examples in connection to the Swampland program in an effort to avoid the geometric lamppost. Additionally, from the non-susy perspective moduli stabilization is an important problem. I will show that non-geometric models can provide non-susy tachyon-free examples with a single neutral scalar field, which are a source of instability. References:<ul><li>Z. K. Baykara, Y. Hamada, H.-C. Tarazi and C. Vafa, On the String Landscape Without Hypermultiplets, 2309.15152.</li><li>Z. K. Baykara, H.-C. Tarazi and C. Vafa, The Quasicrystalline String Landscape, 2406.00129.</li><li>Z. K. Baykara, H.-C. Tarazi and C. Vafa, New Non-Susy Tachyon-Free Strings, 2406.00185.</li></ul>

I will discuss non-geometric flux compactifications of string theory on Landau-Ginzburg models that are dual to rigid Calabi-Yau manifolds. Minkowski vacua can be analyzed even at strong coupling, providing a rare window in this corner of the string theory landscape. We focus on the number of stabilized moduli to test the tadpole conjecture in this context. While the conjecture is confirmed, a refined version is violated and needs to be modified. We furthermore discuss the existence of Minkowski vacua in which all scalar fields are stabilized. For some of these vacua all scalars fields are massive, while others have also some massless but stabilized scalar fields.