Abstract
Within the ongoing debate about de Sitter (dS) vacua in string theory, different aspects of explicit dS proposals have come under intense scrutiny. One key ingredient is D7-brane gaugino condensation, which is usually treated using effective 4d supergravity. However, it is clearly more desirable to derive the relevant scalar potential directly from a local 10d Lagrangian. Such a local 10d description captures the interactions among the various localized sources and the background fields which are smeared in the 4d Lagrangian. While progress in this endeavour has recently been made, some form of non-locality related to the 4-gaugino term has remained hidden in the available proposals. We spell out the local counterterm removing the divergence that arises when integrating out the 3-form flux and which, upon dimensional reduction, serves to reproduce the relevant part of the 4d supergravity action. This is both a step towards a more complete understanding of 10d type-IIB supergravity as well as specifically towards better control of dS constructions in string theory involving gaugino condensation.
References
J. P. Derendinger, L. E. Ibáñez and H. P. Nilles, On the low-energy d = 4, N = 1 supergravity theory extracted from the d = 10, N = 1 superstring, Phys. Lett. B 155 (1985) 65 [INSPIRE].
M. Dine, R. Rohm, N. Seiberg and E. Witten, Gluino condensation in superstring models, Phys. Lett. B 156 (1985) 55 [INSPIRE].
L. E. Ibanez and A. M. Uranga, String theory and particle physics: an introduction to string phenomenology, Cambridge University Press, Cambridge, U.K. (2012).
S. Kachru, R. Kallosh, A. D. Linde and S. P. Trivedi, De Sitter vacua in string theory, Phys. Rev. D 68 (2003) 046005 [hep-th/0301240] [INSPIRE].
V. Balasubramanian, P. Berglund, J. P. Conlon and F. Quevedo, Systematics of moduli stabilisation in Calabi-Yau flux compactifications, JHEP 03 (2005) 007 [hep-th/0502058] [INSPIRE].
U. H. Danielsson and T. Van Riet, What if string theory has no de Sitter vacua?, Int. J. Mod. Phys. D 27 (2018) 1830007 [arXiv:1804.01120] [INSPIRE].
G. Obied, H. Ooguri, L. Spodyneiko and C. Vafa, De Sitter space and the swampland, arXiv:1806.08362 [INSPIRE].
S. K. Garg and C. Krishnan, Bounds on slow roll and the de Sitter swampland, JHEP 11 (2019) 075 [arXiv:1807.05193] [INSPIRE].
H. Ooguri, E. Palti, G. Shiu and C. Vafa, Distance and de Sitter conjectures on the swampland, Phys. Lett. B 788 (2019) 180 [arXiv:1810.05506] [INSPIRE].
J. Moritz, A. Retolaza and A. Westphal, Toward de Sitter space from ten dimensions, Phys. Rev. D 97 (2018) 046010 [arXiv:1707.08678] [INSPIRE].
Y. Hamada, A. Hebecker, G. Shiu and P. Soler, On brane gaugino condensates in 10d, JHEP 04 (2019) 008 [arXiv:1812.06097] [INSPIRE].
R. Kallosh, Gaugino condensation and geometry of the perfect square, Phys. Rev. D 99 (2019) 066003 [arXiv:1901.02023] [INSPIRE].
Y. Hamada, A. Hebecker, G. Shiu and P. Soler, Understanding KKLT from a 10d perspective, JHEP 06 (2019) 019 [arXiv:1902.01410] [INSPIRE].
F. Carta, J. Moritz and A. Westphal, Gaugino condensation and small uplifts in KKLT, JHEP 08 (2019) 141 [arXiv:1902.01412] [INSPIRE].
F. F. Gautason, V. Van Hemelryck, T. Van Riet and G. Venken, A 10d view on the KKLT AdS vacuum and uplifting, JHEP 06 (2020) 074 [arXiv:1902.01415] [INSPIRE].
I. Bena, M. Graña, N. Kovensky and A. Retolaza, Kähler moduli stabilization from ten dimensions, JHEP 10 (2019) 200 [arXiv:1908.01785] [INSPIRE].
S. Kachru, M. Kim, L. Mcallister and M. Zimet, De Sitter vacua from ten dimensions, arXiv:1908.04788 [INSPIRE].
J. Wess and J. Bagger, Supersymmetry and supergravity, Princeton University Press, Princeton, NJ, U.S.A. (1992).
I. Bena, E. Dudas, M. Graña and S. Lüst, Uplifting runaways, Fortsch. Phys. 67 (2019) 1800100 [arXiv:1809.06861] [INSPIRE].
R. Blumenhagen, D. Kläwer and L. Schlechter, Swampland variations on a theme by KKLT, JHEP 05 (2019) 152 [arXiv:1902.07724] [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].
L. Randall, The boundaries of KKLT, Fortsch. Phys. 68 (2020) 1900105 [arXiv:1912.06693] [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].
X. Gao, A. Hebecker and D. Junghans, Control issues of KKLT, Fortsch. Phys. 68 (2020) 2000089 [arXiv:2009.03914] [INSPIRE].
I. Bena, J. Blåbäck, M. Graña and S. Lüst, The tadpole problem, arXiv:2010.10519 [INSPIRE].
A. Hebecker and S. Leonhardt, Winding uplifts and the challenges of weak and strong SUSY breaking in AdS, JHEP 03 (2021) 284 [arXiv:2012.00010] [INSPIRE].
F. Carta, A. Mininno, N. Righi and A. Westphal, Gopakumar-Vafa hierarchies in winding inflation and uplifts, JHEP 05 (2021) 271 [arXiv:2101.07272] [INSPIRE].
F. Carta and J. Moritz, Resolving spacetime singularities in flux compactifications & KKLT, arXiv:2101.05281 [INSPIRE].
D. Andriot, P. Marconnet and D. Tsimpis, Warp factor and the gravitational wave spectrum, JCAP 07 (2021) 040 [arXiv:2103.09240] [INSPIRE].
Y. Honma and H. Otsuka, Small flux superpotential in F-theory compactifications, Phys. Rev. D 103 (2021) 126022 [arXiv:2103.03003] [INSPIRE].
I. Bena, J. Blåbäck, M. Graña and S. Lüst, Algorithmically solving the tadpole problem, arXiv:2103.03250 [INSPIRE].
M.-S. Seo, Dilaton stabilization in KKLT revisited, Nucl. Phys. B 968 (2021) 115452 [arXiv:2103.00811] [INSPIRE].
G. B. De Luca, E. Silverstein and G. Torroba, Hyperbolic compactification of M-theory and de Sitter quantum gravity, arXiv:2104.13380 [INSPIRE].
B. V. Bento, D. Chakraborty, S. L. Parameswaran and I. Zavala, A new de Sitter solution with a weakly warped deformed conifold, arXiv:2105.03370 [INSPIRE].
P. G. Cámara, L. E. Ibáñez and A. M. Uranga, Flux-induced SUSY-breaking soft terms on D7-D3 brane systems, Nucl. Phys. B 708 (2005) 268 [hep-th/0408036] [INSPIRE].
P. Koerber and L. Martucci, From ten to four and back again: how to generalize the geometry, JHEP 08 (2007) 059 [arXiv:0707.1038] [INSPIRE].
D. Baumann, A. Dymarsky, S. Kachru, I. R. Klebanov and L. McAllister, Compactification effects in D-brane inflation, Phys. Rev. Lett. 104 (2010) 251602 [arXiv:0912.4268] [INSPIRE].
D. Baumann, A. Dymarsky, S. Kachru, I. R. Klebanov and L. McAllister, D3-brane potentials from fluxes in AdS/CFT, JHEP 06 (2010) 072 [arXiv:1001.5028] [INSPIRE].
A. Dymarsky and L. Martucci, D-brane non-perturbative effects and geometric deformations, JHEP 04 (2011) 061 [arXiv:1012.4018] [INSPIRE].
M. Graña, N. Kovensky and A. Retolaza, Gaugino mass term for D-branes and generalized complex geometry, JHEP 06 (2020) 047 [arXiv:2002.01481] [INSPIRE].
P. Hořava and E. Witten, Heterotic and type-I string dynamics from eleven-dimensions, Nucl. Phys. B 460 (1996) 506 [hep-th/9510209] [INSPIRE].
P. Hořava and E. Witten, Eleven-dimensional supergravity on a manifold with boundary, Nucl. Phys. B 475 (1996) 94 [hep-th/9603142] [INSPIRE].
P. Hořava, Gluino condensation in strongly coupled heterotic string theory, Phys. Rev. D 54 (1996) 7561 [hep-th/9608019] [INSPIRE].
E. A. Mirabelli and M. E. Peskin, Transmission of supersymmetry breaking from a four-dimensional boundary, Phys. Rev. D 58 (1998) 065002 [hep-th/9712214] [INSPIRE].
A. Falkowski, H. M. Lee and C. Lüdeling, Gravity mediated supersymmetry breaking in six dimensions, JHEP 10 (2005) 090 [hep-th/0504091] [INSPIRE].
S. B. Giddings and A. Maharana, Dynamics of warped compactifications and the shape of the warped landscape, Phys. Rev. D 73 (2006) 126003 [hep-th/0507158] [INSPIRE].
G. Shiu, G. Torroba, B. Underwood and M. R. Douglas, Dynamics of warped flux compactifications, JHEP 06 (2008) 024 [arXiv:0803.3068] [INSPIRE].
M. R. Douglas, Effective potential and warp factor dynamics, JHEP 03 (2010) 071 [arXiv:0911.3378] [INSPIRE].
F. Marchesano, P. McGuirk and G. Shiu, Open string wavefunctions in warped compactifications, JHEP 04 (2009) 095 [arXiv:0812.2247] [INSPIRE].
F. Marchesano, P. McGuirk and G. Shiu, Chiral matter wavefunctions in warped compactifications, JHEP 05 (2011) 090 [arXiv:1012.2759] [INSPIRE].
P. McGuirk, G. Shiu and F. Ye, Soft branes in supersymmetry-breaking backgrounds, JHEP 07 (2012) 188 [arXiv:1206.0754] [INSPIRE].
M. Graña, R. Minasian, M. Petrini and A. Tomasiello, Supersymmetric backgrounds from generalized Calabi-Yau manifolds, JHEP 08 (2004) 046 [hep-th/0406137] [INSPIRE].
D. Lüst, F. Marchesano, L. Martucci and D. Tsimpis, Generalized non-supersymmetric flux vacua, JHEP 11 (2008) 021 [arXiv:0807.4540] [INSPIRE].
S. B. Giddings, S. Kachru and J. Polchinski, Hierarchies from fluxes in string compactifications, Phys. Rev. D 66 (2002) 106006 [hep-th/0105097] [INSPIRE].
M. Nakahara, Geometry, topology and physics, CRC press, U.S.A. (2003).
D. Huybrechts, Complex geometry: an introduction, Springer, Berlin, Heidelberg, Germany (2005).
D. Z. Freedman and A. Van Proeyen, Supergravity, Cambridge University Press, Cambridge, U.K. (2012).
A. Van Proeyen, Tools for supersymmetry, Ann. U. Craiova Phys. 9 (1999) 1 [hep-th/9910030] [INSPIRE].
C. Beasley, J. J. Heckman and C. Vafa, GUTs and exceptional branes in F-theory. Part I, JHEP 01 (2009) 058 [arXiv:0802.3391] [INSPIRE].
T. W. Grimm and J. Louis, The effective action of N = 1 Calabi-Yau orientifolds, Nucl. Phys. B 699 (2004) 387 [hep-th/0403067] [INSPIRE].
A. Retolaza, J. Rogers, R. Tatar and F. Tonioni, Branes, fermions, and superspace dualities, arXiv:2106.02090 [INSPIRE].
M. Berkooz, M. R. Douglas and R. G. Leigh, Branes intersecting at angles, Nucl. Phys. B 480 (1996) 265 [hep-th/9606139] [INSPIRE].
R. Donagi and M. Wijnholt, Model building with F-theory, Adv. Theor. Math. Phys. 15 (2011) 1237 [arXiv:0802.2969] [INSPIRE].
A. Strominger, Superstrings with torsion, Nucl. Phys. B 274 (1986) 253 [INSPIRE].
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Hamada, Y., Hebecker, A., Shiu, G. et al. Completing the D7-brane local gaugino action. J. High Energ. Phys. 2021, 33 (2021). https://doi.org/10.1007/JHEP11(2021)033
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DOI: https://doi.org/10.1007/JHEP11(2021)033
Keywords
- Strings and branes phenomenology