Abstract
We give a comprehensive treatment of the scalar potential for a D3-brane in a warped conifold region of a compactification with stabilized moduli. By studying general ultraviolet perturbations in supergravity, we systematically incorporate ‘compactification effects’ sourced by supersymmetry breaking in the compact space. Significant contributions to the D3-brane potential, including the leading term in the infrared, arise from imaginary anti-self-dual (IASD) fluxes. For an arbitrary Calabi-Yau cone, we determine the most general IASD fluxes in terms of scalar harmonics, then compute the resulting D3-brane potential. Specializing to the conifold, we identify the operator dual to each mode of flux, and for chiral operators we confirm that the potential computed in the gauge theory matches the gravity result. The effects of four-dimensional curvature, including the leading D3-brane mass term, arise directly from the ten-dimensional equations of motion. Furthermore, we show that gaugino condensation on D7-branes provides a local source for IASD flux. This flux automatically and precisely encodes the nonperturbative contributions to the D3-brane potential, yielding a promising ten-dimensional representation of four-dimensional nonperturbative effects. Our result encompasses all significant contributions to the D3-brane potential discussed in the literature, and does so in the single coherent framework of ten-dimensional supergravity. Moreover, we identify new terms with irrational scaling dimensions that were inaccessible in prior works. By decoupling gravity in a noncompact configuration, then systematically reincorporating compactification effects as ultraviolet perturbations, we have provided an approach in which Planck-suppressed contributions to the D3-brane effective action can be computed. This is the companion paper to [1].
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D. Baumann, A. Dymarsky, S. Kachru, I.R. Klebanov and L. McAllister, Compactification effects in D-brane ination, arXiv:0912.4268 [SPIRES].
WMAP collaboration, E. Komatsu et al., Five-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: cosmological interpretation, Astrophys. J. Suppl. 180 (2009) 330 [arXiv:0803.0547] [SPIRES].
A.H. Guth, The inationary universe: a possible solution to the horizon and flatness problems, Phys. Rev. D 23 (1981) 347 [SPIRES].
A.D. Linde, A new inationary universe scenario: a possible solution of the horizon, atness, homogeneity, isotropy and primordial monopole problems, Phys. Lett. B 108 (1982) 389 [SPIRES].
A. Albrecht and P.J. Steinhardt, Cosmology for grand unified theories with radiatively induced symmetry breaking, Phys. Rev. Lett. 48 (1982) 1220 [SPIRES].
CMBPol Study Team collaboration, D. Baumann et al., CMBPol mission concept study: probing inflation with CMB polarization, AIP Conf. Proc. 1141 (2009) 10 [arXiv:0811.3919] [SPIRES].
D. Baumann, TASI lectures on inflation, arXiv:0907.5424 [SPIRES].
D. Baumann and L. McAllister, Advances in inflation in string theory, Ann. Rev. Nucl. Part. Sci. 59 (2009) 67 [arXiv:0901.0265] [SPIRES].
S. Kachru et al., Towards inflation in string theory, JCAP 10 (2003) 013 [hep-th/0308055] [SPIRES].
J.M. Cline, String cosmology, hep-th/0612129 [SPIRES].
C.P. Burgess, Lectures on cosmic inflation and its potential stringy realizations, PoS P 2GC (2006) 008 [arXiv:0708.2865] [SPIRES].
L. McAllister and E. Silverstein, String cosmology: a review, Gen. Rel. Grav. 40 (2008) 565 [arXiv:0710.2951] [SPIRES].
I.R. Klebanov and M.J. Strassler, Supergravity and a confining gauge theory: Duality cascades and χ SB -resolution of naked singularities, JHEP 08 (2000) 052 [hep-th/0007191] [SPIRES].
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] [SPIRES].
D. Baumann et al., On D3-brane potentials in compactifications with fluxes and wrapped D-branes, JHEP 11 (2006) 031 [hep-th/0607050] [SPIRES].
D. Baumann, A. Dymarsky, I.R. Klebanov and L. McAllister, Towards an explicit model of D-brane inflation, JCAP 01 (2008) 024 [arXiv:0706.0360] [SPIRES].
D. Baumann, A. Dymarsky, S. Kachru, I.R. Klebanov and L. McAllister, Holographic systematics of D-brane inflation, JHEP 03 (2009) 093 [arXiv:0808.2811] [SPIRES].
A. Buchel and R. Roiban, Inflation in warped geometries, Phys. Lett. B 590 (2004) 284 [hep-th/0311154] [SPIRES].
A. Buchel, Inflation on the resolved warped deformed conifold, Phys. Rev. D 74 (2006) 046009 [hep-th/0601013] [SPIRES].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [SPIRES].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [SPIRES].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [SPIRES].
A. Ceresole, G. Dall'Agata, R. D'Auria and S. Ferrara, Spectrum of type IIB supergravity on AdS 5 × T 11: predictions on N = 1 SCFT's, Phys. Rev. D 61 (2000) 066001 [hep-th/9905226] [SPIRES].
E. Witten, Non-perturbative superpotentials in string theory, Nucl. Phys. B 474 (1996) 343 [hep-th/9604030] [SPIRES].
M. Berg, M. Haack and B. Körs, Loop corrections to volume moduli and inflation in string theory, Phys. Rev. D 71 (2005) 026005 [hep-th/0404087] [SPIRES].
M. Graña, MSSM parameters from supergravity backgrounds, Phys. Rev. D 67 (2003) 066006 [hep-th/0209200] [SPIRES].
P. Koerber and L. Martucci, From ten to four and back again: how to generalize the geometry, JHEP 08 (2007) 059 [arXiv:0707.1038] [SPIRES].
D. Baumann, A. Dymarsky, S. Kachru, I. R. Klebanov and L. McAllister, Flux duals of non-perturbative effects on D7-branes, work in progress.
I.R. Klebanov and E. Witten, Superconformal field theory on threebranes at a Calabi-Yau singularity, Nucl. Phys. B 536 (1998) 199 [hep-th/9807080] [SPIRES].
S.B. Giddings, S. Kachru and J. Polchinski, Hierarchies from fluxes in string compactifications, Phys. Rev. D 66 (2002) 106006 [hep-th/0105097] [SPIRES].
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] [SPIRES].
G. Shiu, G. Torroba, B. Underwood and M.R. Douglas, Dynamics of warped flux compactifications, JHEP 06 (2008) 024 [arXiv:0803.3068] [SPIRES].
M. Haack et al., Update of D3/D7-brane inflation on K3 × T 2/Z 2, Nucl. Phys. B 806 (2009) 103 [arXiv:0804.3961] [SPIRES].
O. DeWolfe, S. Kachru and M. Mulligan, A gravity dual of metastable dynamical supersymmetry breaking, Phys. Rev. D 77 (2008) 065011 [arXiv:0801.1520] [SPIRES].
I. Bena, M. Graña and N. Halmagyi, On the existence of meta-stable vacua in Klebanov-Strassler, arXiv:0912.3519 [SPIRES].
A. Butti, M. Graña, R. Minasian, M. Petrini and A. Zaffaroni, The baryonic branch of Klebanov-Strassler solution: a supersymmetric family of SU(3) structure backgrounds, JHEP 03 (2005) 069 [hep-th/0412187] [SPIRES].
C.P. Herzog, I.R. Klebanov and P. Ouyang, Remarks on the warped deformed conifold, hep-th/0108101 [SPIRES].
S. Kuperstein and J. Sonnenschein, Analytic non-supersymmetric background dual of a confining gauge theory and the corresponding plane wave theory of hadrons, JHEP 02 (2004) 015 [hep-th/0309011] [SPIRES].
I.R. Klebanov and A. Murugan, Gauge/gravity duality and warped resolved conifold, JHEP 03 (2007) 042 [hep-th/0701064] [SPIRES].
D. Baumann and L. McAllister, A microscopic limit on gravitational waves from D-brane inflation, Phys. Rev. D 75 (2007) 123508 [hep-th/0610285] [SPIRES].
D. Baumann, A. Dymarsky, I.R. Klebanov, L. McAllister and P.J. Steinhardt, A delicate universe, Phys. Rev. Lett. 99 (2007) 141601 [arXiv:0705.3837] [SPIRES].
A. Krause and E. Pajer, Chasing brane inflation in string-theory, JCAP 07 (2008) 023 [arXiv:0705.4682] [SPIRES].
I.R. Klebanov and A.A. Tseytlin, Gravity duals of supersymmetric SU(N) × SU(N +M) gauge theories, Nucl. Phys. B 578 (2000) 123 [hep-th/0002159] [SPIRES].
A. Ceresole, G. Dall'Agata and R. D'Auria, KK spectroscopy of type IIB supergravity on AdS 5 × T 11, JHEP 11 (1999) 009 [hep-th/9907216] [SPIRES].
S.S. Gubser, Einstein manifolds and conformal field theories, Phys. Rev. D 59 (1999) 025006 [hep-th/9807164] [SPIRES].
F. Cachazo, M.R. Douglas, N. Seiberg and E. Witten, Chiral rings and anomalies in supersymmetric gauge theory, JHEP 12 (2002) 071 [hep-th/0211170] [SPIRES].
P.G. Camara, 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] [SPIRES].
S. Benvenuti, M. Mahato, L.A. Pando Zayas and Y. Tachikawa, The gauge/gravity theory of blown up four cycles, hep-th/0512061 [SPIRES].
I. Gordeli and D. Melnikov, On I-even singlet glueballs in the Klebanov-Strassler theory, arXiv:0912.5517 [SPIRES].
M. Graña and J. Polchinski, Supersymmetric three-form flux perturbations on AdS 5, Phys. Rev. D 63 (2001) 026001 [hep-th/0009211] [SPIRES].
P. Ouyang, Holomorphic D7-branes and flavored N = 1 gauge theories, Nucl. Phys. B 699 (2004) 207 [hep-th/0311084] [SPIRES].
S. Kuperstein, Meson spectroscopy from holomorphic probes on the warped deformed conifold, JHEP 03 (2005) 014 [hep-th/0411097] [SPIRES].
S. Gukov, C. Vafa and E. Witten, CFT's from Calabi-Yau four-folds, Nucl. Phys. B 584 (2000) 69 [hep-th/9906070] [SPIRES].
O. DeWolfe and S.B. Giddings, Scales and hierarchies in warped compactifications and brane worlds, Phys. Rev. D 67 (2003) 066008 [hep-th/0208123] [SPIRES].
O.J. Ganor, On zeroes of superpotentials in F-theory, Nucl. Phys. Proc. Suppl. 67 (1998) 25 [SPIRES].
A. Dymarsky and L. Martucci, Nonperturbative effects on D7-branes and geometric deformations, work in progress.
A.R. Frey and M. Lippert, AdS strings with torsion: non-complex heterotic compactifications, Phys. Rev. D 72 (2005) 126001 [hep-th/0507202] [SPIRES].
D. Lüst, S. Reffert, W. Schulgin and P.K. Tripathy, Fermion zero modes in the presence of fluxes and a non-perturbative superpotential, JHEP 08 (2006) 071 [hep-th/0509082] [SPIRES].
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] [SPIRES].
P. Griffiths and J. Harris, Principles of algebraic geometry, Wiley & Sons, U.S.A. (1978).
F. Marchesano and L. Martucci, Non-perturbative effects on seven-brane Yukawa couplings, arXiv:0910.5496 [SPIRES].
C. Vafa, Superstrings and topological strings at large-N, J. Math. Phys. 42 (2001) 2798 [hep-th/0008142] [SPIRES].
J.M. Maldacena and C. Núñez, Towards the large-N limit of pure N = 1 super Yang-Mills, Phys. Rev. Lett. 86 (2001) 588 [hep-th/0008001] [SPIRES].
S. Cecotti, M.C.N. Cheng, J.J. Heckman and C. Vafa, Yukawa couplings in F-theory and non-commutative geometry, arXiv:0910.0477 [SPIRES].
R.C. Myers, Dielectric-branes, JHEP 12 (1999) 022 [hep-th/9910053] [SPIRES].
B.A. Burrington, J.T. Liu, L.A. Pando Zayas and D. Vaman, Holographic duals of flavored N = 1 super Yang-Mills: beyond the probe approximation, JHEP 02 (2005) 022 [hep-th/0406207] [SPIRES].
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ArXiv ePrint: 1001.5028
On leave of absence from Stanford University and SLAC.
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Baumann, D., Dymarsky, A., Kachru, S. et al. D3-brane potentials from fluxes in AdS/CFT. J. High Energ. Phys. 2010, 72 (2010). https://doi.org/10.1007/JHEP06(2010)072
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DOI: https://doi.org/10.1007/JHEP06(2010)072