Abstract
We study sigma models in AdS4 with global \( \mathcal{N} = {1} \) supersymmetry and find that they differ significantly from their flat-space cousins — the target space is constrained to be a Kähler manifold with an exact Kähler form, the superpotential transforms under Kähler transformations, the space of supersymmetric vacua is generically a set of isolated points even when the superpotential vanishes, and the R-symmetry is classically broken by the cosmological constant. Remarkably, the exactness of the Kähler class is also required for the sigma model to arise as a decoupling limit of \( \mathcal{N} = {1} \) supergravity, and ensures the vanishing of gravitational anomalies. As applications of these results, we argue that fields with AdS4 scale masses are ubiquitous in, for example, type IIB \( \mathcal{N} = {1} \) AdS4 vacua stabilized near large volume; we also present a schematic argument that the Affleck-Dine-Seiberg runaway of N f < N c SQCD can be regulated by considering the theory in AdS4.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M.R. Douglas and S. Kachru, Flux compactification, Rev. Mod. Phys. 79 (2007) 733 [hep-th/0610102] [INSPIRE].
R. Blumenhagen, B. Körs, D. Lüst and S. Stieberger, Four-dimensional string compactifications with D-branes, orientifolds and fluxes, Phys. Rept. 445 (2007) 1 [hep-th/0610327] [INSPIRE].
F. Denef, Les Houches lectures on constructing string vacua, arXiv:0803.1194 [INSPIRE].
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].
Z. Komargodski and N. Seiberg, Comments on supercurrent multiplets, supersymmetric field theories and supergravity, JHEP 07 (2010) 017 [arXiv:1002.2228] [INSPIRE].
A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nicolis and R. Rattazzi, Causality, analyticity and an IR obstruction to UV completion, JHEP 10 (2006) 014 [hep-th/0602178] [INSPIRE].
I. Affleck, M. Dine and N. Seiberg, Dynamical supersymmetry breaking in supersymmetric QCD, Nucl. Phys. B 241 (1984) 493.
O. Aharony, M. Berkooz, D. Tong, and S. Yankielowicz, work in progress.
E. Witten and J. Bagger, Quantization of Newton’s constant in certain supergravity theories, Phys. Lett. B 115 (1982) 202.
B. Keck, An alternative class of supersymmetries, J. Phys. A 8 (1975) 1819.
B. Zumino, Nonlinear realization of supersymmetry in Anti de Sitter space, Nucl. Phys. B 127 (1977) 189.
E. Ivanov and A.S. Sorin, Wess-Zumino model as linear σ-model of spontaneously broken conformal and OSp(1, 4) supersymmetries, Sov. J. Nucl. Phys. 30 (1979) 440 [INSPIRE].
E. Ivanov and A.S. Sorin, Superfield formulation of Osp(1,4) supersymmetry, J. Phys. A 13 (1980) 1159 [INSPIRE].
P. Breitenlohner and D.Z. Freedman, Positive energy in anti-de Sitter backgrounds and gauged extended supergravity, Phys. Lett. B 115 (1982) 197 [INSPIRE].
C.J. Burges, D.Z. Freedman, S. Davis and G. Gibbons, Supersymmetry in anti-de Sitter space, Annals Phys. 167 (1986) 285 [INSPIRE].
B. de Wit and I. Herger, Anti-de Sitter supersymmetry, Lect. Notes Phys. 541 (2000) 79 [hep-th/9908005] [INSPIRE].
D. McKeon and C. Schubert, Supersymmetry on AdS 3 and AdS 4, Class. Quant. Grav. 21 (2004) 3337 [hep-th/0301225] [INSPIRE].
B. Gripaios, H.D. Kim, R. Rattazzi, M. Redi and C. Scrucca, Gaugino mass in AdS space, JHEP 02 (2009) 043 [arXiv:0811.4504] [INSPIRE].
R. Rattazzi and M. Redi, Gauge boson mass generation in AdS 4, JHEP 12 (2009) 025 [arXiv:0908.4150] [INSPIRE].
O. Aharony, D. Marolf and M. Rangamani, Conformal field theories in Anti-de Sitter space, JHEP 02 (2011) 041 [arXiv:1011.6144] [INSPIRE].
J. Donoghue, E. Golowich, and B. R. Holstein, Dynamics of the standard model, Camb. Monogr. Part. Phys. Nucl. Phys. Cosmol. 2 (1992) 1.
J. Wess and J. Bagger, Supersymmetry and supergravity, Princeton University Press, Princeton U.S.A. (1992).
R. Harvey and H.B. Lawson, Calibrated geometries, Acta Mathematica 148 (1982) 47.
S. Weinberg, The quantum theory of fields. Vol. 3: supersymmetry, Cambridge University Press, Cambridge U.K. (2000).
A.E. Nelson and N. Seiberg, R symmetry breaking versus supersymmetry breaking, Nucl. Phys. B 416 (1994) 46 [hep-ph/9309299] [INSPIRE].
C.G. Callan Jr. and F. Wilczek, Infrared behavior at negative curvature, Nucl. Phys. B 340 (1990) 366 [INSPIRE].
A.J. Amsel and D. Marolf, Supersymmetric multi-trace boundary conditions in AdS, Class. Quant. Grav. 26 (2009) 025010 [arXiv:0808.2184] [INSPIRE].
D. Butter and S.M. Kuzenko, \( \mathcal{N} = {2} \) AdS supergravity and supercurrents, JHEP 07 (2011) 081 [arXiv:1104.2153] [INSPIRE].
S. Ferrara and B. Zumino, Transformation properties of the supercurrent, Nucl. Phys. B 87 (1975) 207 [INSPIRE].
G.W. Moore and P.C. Nelson, The etiology of sigma model anomalies, Commun. Math. Phys. 100 (1985) 83.
J. Distler and E. Sharpe, Quantization of Fayet-Iliopoulos parameters in supergravity, Phys. Rev. D 83 (2011) 085010 [arXiv:1008.0419] [INSPIRE].
S. Kachru, R. Kallosh, A.D. Linde, J.M. Maldacena, L.P. McAllister, et al., Towards inflation in string theory, JCAP 10 (2003) 013 [hep-th/0308055] [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].
D. Lüst and D. Tsimpis, Classes of AdS 4 type IIA / IIB compactifications with SU(3) × SU(3) structure, JHEP 04 (2009) 111 [arXiv:0901.4474] [INSPIRE].
D. Lüst and D. Tsimpis, New supersymmetric AdS 4 type-II vacua, JHEP 09 (2009) 098 [arXiv:0906.2561] [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].
J.P. Conlon, F. Quevedo and K. Suruliz, Large-volume flux compactifications: moduli spectrum and D3/D7 soft supersymmetry breaking, JHEP 08 (2005) 007 [hep-th/0505076] [INSPIRE].
O. DeWolfe and S.B. Giddings, Scales and hierarchies in warped compactifications and brane worlds, Phys. Rev. D 67 (2003) 066008 [hep-th/0208123] [INSPIRE].
P.G. Camara, L. Ibáñez and A. Uranga, Flux induced SUSY breaking soft terms, Nucl. Phys. B 689 (2004) 195 [hep-th/0311241] [INSPIRE].
M. Graña, T.W. Grimm, H. Jockers and J. Louis, Soft supersymmetry breaking in Calabi-Yau orientifolds with D-branes and fluxes, Nucl. Phys. B 690 (2004) 21 [hep-th/0312232] [INSPIRE].
D. Baumann, A. Dymarsky, I.R. Klebanov, J.M. Maldacena, L.P. McAllister, et al., On D3-brane potentials in compactifications with fluxes and wrapped D-branes, JHEP 11 (2006) 031 [hep-th/0607050] [INSPIRE].
E. Witten, Nonperturbative superpotentials in string theory, Nucl. Phys. B 474 (1996) 343 [hep-th/9604030] [INSPIRE].
K.A. Intriligator and N. Seiberg, Lectures on supersymmetric gauge theories and electric-magnetic duality, Nucl. Phys. Proc. Suppl. 45BC (1996) 1 [hep-th/9509066] [INSPIRE].
N. Seiberg, Naturalness versus supersymmetric nonrenormalization theorems, Phys. Lett. B 318 (1993) 469 [hep-ph/9309335] [INSPIRE].
S. Hellerman and E. Sharpe, Sums over topological sectors and quantization of Fayet-Iliopoulos parameters, arXiv:1012.5999 [INSPIRE].
P. Adamietz, P. Binetruy, G. Girardi and R. Grimm, Supergravity and matter: linear multiplet couplings and Kähler anomaly cancellation, Nucl. Phys. B 401 (1993) 257 [INSPIRE].
P. Griffiths and J. Harris, Principles of algebraic geometry, John Wiley & Sons, New York U.S.A. (1994).
T. Banks and N. Seiberg, Symmetries and strings in field theory and gravity, Phys. Rev. D 83 (2011) 084019 [arXiv:1011.5120] [INSPIRE].
R. Bott and L.W. Tu, Differential forms in algebraic topology, Graduate Texts in Mathematics, Springer, Berlin Germany (1982).
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1104.3155
Rights and permissions
About this article
Cite this article
Adams, A., Jockers, H., Kumar, V. et al. \( \mathcal{N} = {1} \) sigma models in AdS4 . J. High Energ. Phys. 2011, 42 (2011). https://doi.org/10.1007/JHEP12(2011)042
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2011)042