Flux supersymmetry breaking in MSSM string compacti¯cations Angel M. Uranga IFT-UAM/CSIC, Madrid EuroGDR meeting, Frascati, November 27th, 2004 Plan of the talk Motivation ² Overview of flux compacti¯cations ² MSSM Model building ² Flux susy breaking and soft terms ² Conclusions ² Motivation Recent great interest in backgrounds/compacti¯cations of string/M - ² theory with non-trivial ¯eld strength fluxes for diverse p-form ¯elds F = @ C ¹1:::¹p+1 [¹p+1 ¹1:::¹p] PICTURE: F p+1 =dC p Non−compact 4d [M 4, dS 4, AdS 4 ] Natural possibility in the construction, not exploited until recently ² These constructions lead to new and interesting features, compared with ² previous compacti¯cations - Stabilization of moduli - Warped compacti¯cations - Breaking of supersymmetry In a computable regime! AIM: Overview of these aspects in a well-studied class of models Type IIB string theory compacti¯ed on CY3 with NSNS/RR 3-form fluxes H3, F3 With an eye on phenomenological applications Type IIB on CY3 orientifolds A very general set of models with 4d N = 1 supersymmetry F-theory on CY4, or equivalent description in terms of Type IIB string theory, 10d massless ¯elds: NSNS G , B , © ! MN MN RR a, B~ , C ! MN MNP Q Contains a number of solitonic objects (D-branes) with gauge ¯elds local- ized on their volume Background includes following ingredients IIB compacti¯ed on M CY ² 4£ 3 Stacks of 7-branes wrapped on 4-cycles ² O3-planes ² D3-branes at points on CY ² 3 Type IIB on CY3 orientifolds X6 M4 Background includes following ingredients IIB compacti¯ed on M CY ² 4£ 3 Type IIB on CY3 orientifolds X6 D7 M4 Background includes following ingredients IIB compacti¯ed on M CY ² 4£ 3 Stacks of 7-branes wrapped on 4-cycles ² Type IIB on CY3 orientifolds X6 D7 M4 O3 Background includes following ingredients IIB compacti¯ed on M CY ² 4£ 3 Stacks of 7-branes wrapped on 4-cycles ² Quotient by an orientifold action: introduces O3-planes, ² Type IIB on CY3 orientifolds X6 D7 M4 O3 D3 Background includes following ingredients IIB compacti¯ed on M CY ² 4£ 3 Stacks of 7-branes wrapped on 4-cycles ² Quotient by an orientifold action: introduces O3-planes, ² objects of equal negative tension and RR 4-form charge D3-branes, objects of equal positive tension and RR 4-form charge ² Obs: Changes and tensions of D3- and O3- cancel and allow for M4 com- pacti¯cation. Moduli in these models Nice setup for model building, 4d N = 1 susy, and possibly realistic gauge sectors localized on the D3- and/or D7-branes (see later) Several kinds of moduli: Dilaton-axion ¿ = a + i=gs ² KÄahler moduli: size of 2- and 4-cycles ² Complex structure moduli: size of 3-cycles ² D-brane moduli: D-brane positions (and world-volume gauge ¯eld data) ² X6 M4 How to get rid of these massless scalars? Type IIB on CY3 with 3-form fluxes [Becker's; Dasgupta, Rajesh, Sethi; Giddings, Kachru, Polchinski;...] 10d Type IIB: NSNS G , B , © ! MN MN RR a, B~ , C ! MN MNP Q Consider compacti¯cation to 4d on a 6d CY3, with non-trivial background for internal components of NSNS/RR ¯eld strength 3-forms H3 , F3 X 6 H3 F 3 M4 Convenient to de¯ne the complex flux density G = F ¿H 3 3 ¡ 3 Fluxes have an energy density 6 lmn Eflux = d x (G3)lmn(G3) = G3 6G3 ZX6 ZX6 ^ ¤ Fluxes are charged under the RR 4-form 6 Qflux = i d x ²lmnpqr(G3)lmn(G3)pqr = i G3 G3 ¡ ZX6 ¡ ZX6 ^ Cancellation of 4-form charge requires Q + Q Q = 0 flux D3 ¡ O3 Notice that for G = iG , tension equals charge, E = Q . ¤6 3 3 flux flux Charge cancellation implies cancellation of tension for ISD G3 Compacti¯cation to M with zero c.c. (at leading approximation). ! 4 Conditions to have a consistent con¯guration Bianchi identities: dH = 0, dF = 0 (fluxes have no sources) ² 3 3 Flux quantization ² For a basis of 3-cycles §a, H Z, F Z §a 3 2 §a 3 2 R R RR tadpole cancellation: Total C -charge in compact CY = 0 ² 4 3 Q + Q Q = 0 flux D3 ¡ O3 Minimization of potential energy (scalar potential) ² W = G ­ [Gukov, Vafa, Witten] CY3 3 ^ V = E +R T T = G i G 2 flux D3 ¡ O3 CY3 j 3 ¡ ¤ 3j R Minima of potential G3 = i 6d G3 Flux density is ISD Moduli stabilization! ¤ -!Since fluxes are quantized, their integrals over 3-cycles are ¯xed, and the flux density depends on complex structure moduli. - In addition G3 depends explicitly on ¿. Generically, stabilization of 10d dilaton and complex structure moduli. ! KÄahler moduli are not stabilized. 4d e®ective theory description 4d e®ective action in terms of K(½; ½¹) = 3 log(½ + ½¹) ¡ W (Ái) = G3 ­ ZX6 ^ No-scale supergravity structure K 2 V = e DaW D W¹ 3 W ¹a ¡ j j ³ ´ with DaW = @aW + @aK W . Cancellation leads to V = eK D W 2 j i j V is de¯nite positive, and vanishes for DiW = 0, independently of KÄahler moduli ½. Same number of equations and unknowns generically isolated solutions for dilaton and complex structure vevs. ! Supersymmetry The conditions that a flux combination G3 preserves some supersymmetry are G is (2; 1) ² 3 G is primitive, G J = 0 [Gra~na, Polchinski] ² 3 3 ^ The primitivity condition is automatic in non-trivial CY compacti¯cations (no 5-forms on CY) The condition of ISD allows G3 to have (0; 3) and (2; 1) (2; 1) G flux supersymmetric 4d vacuum ² 3 ! (0; 3) G flux non-supersymmetric, but zero vacuum energy ² 3 ! (to leading order in ®0, gs) IASD G non-supersymmetric, and leads to non-zero vacuum energy ² 3 ! (rather, to runaway potential for KÄahler moduli) Many interesting new issues Questions: Values of moduli masses, vevs, ... ? ² Susy breaking scale in gravit. sector? In SM? Partial answers (and much work needed) by analysis of flux stabilized vacua [Douglas et al.] Full stabilization of all moduli? ² A proposal [Kachru, Kallosh, Linde, Trivedi] Add non-perturbative e®ects to stabilize KÄahler moduli [Add_ susy breaking source (D3's) to lift to dS vacua] Progress towards explicit models? [Denef, Douglas, Florea] Cosmological applications ² Cosmological constant, brane inflation, cosmic strings, ... TODAY: Center on several particle physics questions Where is the (MS)SM? Susy breaking by fluxes and soft terms Phenomenological model building Where is the SM in this picture? Embed the SM in con¯gurations of D-branes in the model ! Take advantange of similar analysis in the absence of fluxes. Chirality is non-trivial Isolated branes at smooth points lead to non-chiral world-volume gauge ! theories. 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Center on supersymmetric sets of D-branes, and non-supersymmetric fluxes Supersymmetry breaking by fluxes manifests as soft supersymmetry break- ing terms on the D-brane gauge sector. Two strategies: D-branes are sensitive only to local background around them.