Dynamical Supersymmetry Breaking in String Models Jason Kumar University of California, Irvine

String Theory, Cosmology and Phenomenology LHC is coming soon, WMAP is here, DM direct and indirect –good chance to probe EWSB, SUSY, dark matter, inflation, etc. goal for string theory –not necessarily to use LHC “prove or falsify string theory” –instead, use string theory to provide insight about lower-energy physics which you can probe at experiments string theory can access gravity, gauge, matter –insights can connect to LHC, cosmology, phenomenology many string models –don’t want to take one specific model and beat it to death –instead, focus on lessons common to many models doesn’t give a “prediction of string theory” –gives a motivated idea for what new physics might look like at the EFT level

String models recent focus Type IIA/B –non-perturbative physics gives many options gauge group, matter multiplicity and representations, etc. –D-branes/open strings are the key need to get chiral matter –branes at singularities –intersecting brane models (IBMs) much work on both… we study IBMs

IBM  Basic Idea compactify IIA/B on orientifolded CY 3-fold –10D  4D ; N=8  N=1 O-planes have spacetime- filling charge  need to cancel (Gauss’ Law / RR-tadpoles) D-branes do the job (D6-brane in IIA) open strings give gauge theory, chiral matter I ab counts bifundamental chiral matter –sym., anti-sym from O-planes tower of string excitations also we want an SM-sector, plus other sectors extra sectors are generic, since we need to cancel charge bifundamental matter is generic, since 3-cycles on a 6- manifold generally intersect

Standard Model example general features we can use –extra sectors with U(1)’s –representations: bifundamental, symmetric, anti-symmetric –SM particles not charged under U(1) X at tree-level pseudo-hidden sector –generic chiral matter mixed anomalies  canceled by Green-Schwarz mechanism cubic anomalies automatically cancel due to Gauss’ Law –many excited string modes U(3) qcd U(1) X SU(2) L U(1) L SU(2) R QLQL L u R,d R eR,nReR,nR

A few different directions…. general phenomenological issues…. –dynamical supersymmetry breaking arXiv: –mediation to Standard Model (w/ S. Kachru, E. Silverstein) LHC collider phenomenology –coupling SM gauge bosons to extra U(1) arXiv: (w/ A. Rajaraman, J. Wells) –modified trilinear WWZ couplings arxiv: (w/ AR, JW) cosmology –inflation hep-th/ (w/ B. Dutta, L. Leblond) non-gaussianity (w/ B. Dutta, L. Leblond) –baryogenesis hep-th/ (w/ B. Dutta) –dark matter (w/ J. Feng)

Dynamical Supersymmetry Breaking would like to generate an exponentially low susy scale by dynamics –not only explain why it’s stable, but why it’s low standard way to generate low scale in EFT –dimensional transmutation –dynamics of non-abelian gauge group generates scale ISS; Kawano, Kitano, Ooguri, Ookouchi, etc. difficulties in gauge mediation –gauge messengers could cause Landau poles [ SU(5)  N C > 5 – 10 ] –more scales (hierarchy between L dyn and m q ) –harder to arrange in simple IBM’s (get N F  N C ) –nice to have other options anyway AKS used D-instanton to generate low scale –no non-Abelian dynamics –inherently “stringy” –fits in with branes at singularities is there something similar for intersecting brane models?

Yukawa coupling in IBM setup, Yukawa coupling arises from worldsheet instantons (Aldazabal, Franco, Ibanez, Rabadan, Uranga; Kachru, Katz, Lawrence, McGreevy; Cremades, Ibanez, Marchesano; Cvetic, Papadimitriou) – l is exponentially suppressed –in large volume regime (where moduli stabilization is understood), we get small number for free this is a stringy effect –from EFT point of view, no reason for l to be small f1f1 f2f2 f3f3 a b c

Use small l to get a small scale D-terms will play a vital role start with a simple example  3 intersecting branes –gauge theories have non- trivial Fayet-Iliopoulos terms –assume they are of some “natural” scale (perhaps GUT) which need not be small ~ x –additional terms due to axions Green-Schwarz mechanism all superpotential terms are non-perturbative –dominated by some small l

Scaling of V F and V D of course, if l=0 we can set V F =V D =0 by sitting on a D-flat direction –take x a,c > 0, x b < 0 D-flat direction - r naturally get l  g –i.e., g small, l exponentially small –V D  V F  x 2 –moving on r is not a runaway direction for V F

Basic points not dependent on specific form of potential or brane configuration W coefficients exponentially suppressed –end up on D-flat direction “corrected” by F-terms more F-term equations than D-flat directions F-term runaway direction is generically not a D-flat direction V D  V F, but V F exponentially suppressed x depends on “hypermultiplet” moduli –need to stabilize to avoid runaway to supersymmetric vacuum –but we need to stabilize closed string moduli anyway for phenomenological reasons we will assume closed string moduli stabilized

How to mediate to SM? consider an SU(5) GUT setup –extra U(1) brane 5 from bifundamental 10 from antisymmetric generic bifund. matter –gauge mediation natural want to include both the SU(5) sector and DSB sector –need to add a few extra branes for anomaly cancellation –also to make sure generic superpotential involves all fields M 1,2  gauge messengers U(5) GUT U(1) 10 5

assume x GUT = 0 to avoid breaking GUT at higher scale –needed in any case, independent of DSB mech. assume one limit for simplicity factors which affect pheno. –scale of F –scale of messenger masses –scale of R-symmetry breaking gaugino masses each controlled by a different Yukawa in this setup involves interplay between D- term and F-term –would be nice to find a version with only F-term dynamics, ala AKS –working on this now….

Dark Matter couple of interesting features inherent to IBM scenario –many hidden gauge sectors –gauge mediation between open string sectors generic (via bifundamental matter) can have stable particles charged only under hidden sector –left over discrete symmetries could stabilize possible dark matter candidates? –no SM charge –if stable, they contribute to dark matter could be either good, or bad what are the general dark matter implications for this type of scenario?

Setup one sector breaks SUSY gauge mediation to multiple sectors, including SM sector unbroken discrete symmetries not a detailed IBM scenario –not worrying about details of genericity, # of sectors, size of Yukawas, discrete symmetries, etc. –looking at a motivated EFT scenario in each sector, low-energy scale set by contribution to fermion/scalar splitting due to gauge interactions –vector-like matter can be expected to get mass at high (GUT) scale –non-vectorlike matter has no mass scale, except that generated by gauge mediation –much as susy-breaking scale in MSSM sets the EWSB scale and everything else (up to small Yukawas) SUSY hidden MSSM

Gauge mediation “WIMP miracle” –stable matter with weak group coupling and EWSB scale mass would lead to approximately the right relic density for dark matter –R-parity can stabilize the LSP expect to be couple with SU(2) strength and with mass ~ EWSB scale in gravity mediation in gauge mediation, gravitino is LSP (very light) –no good DM candidate  gravitino DM density too large –WIMP miracle points to gravity mediation and conserved R-parity lots of work connecting dark matter and the EWSB scale –but is the miracle really so miraculous?

Scaling we assume that F and M mess are set by the dynamics of susy-breaking sector –same for all gauge sectors in each sector, ratio of gauge coupling to scalar mass is approximately fixed same ratio determines annihilation cross-section via gauge interactions –determines relic density –if MSSM gets it right, so does every other sector

Upshot we find in this scenario, a generic charged stable particle should have the right density (order of magnitude) to be dark matter maybe WIMP miracle isn’t that miraculous … any gauge sector with any coupling would have worked in fact, it should have worked for the MSSM in gauge-mediation –two stable particles  the LSP and the electron –first accident  electron Yukawa coupling is extremely (perhaps unnaturally) small mass much lighter than normal scale a “natural” mass would be m top if electron mass were ~ m top, would have the right relic density –second accident  in gauge mediation, the LSP is not gauge charged but in any other sector, a discrete symmetry can stabilize a hidden sector gauge charged particle –in the right ball-park for dark matter –distinct from gravity mediated result, where it really is a miracle

But what about detection? if hidden sector not coupled to visible sector, all DM annihilations could be invisible –in this case, could not detect DM by direct, indirect or collider only by astronomical observation but if hidden sector couples to SM sector, very interesting detection scenarios –could couple to SM particles via Yukawa or gauge couplings –Yukawa coupling especially interesting, as it could be O(1) assume fewer SM final states

Indirect Detection possibilities dark matter at galactic center annihilates to SM particles, which emit photons detected at gamma ray telescopes –photon flux scales as (# density) 2 –larger signal at small M X take scenario with Yukawa coupling to SM –X is the light hidden sector scalar stabilized by discrete symmetry mass ~ 5 GeV –Y is a fermion with both hidden and SM charge gains mass from both hidden and SM gauge interactions mass ~ 1 TeV coupled to SM up-quarks –W = lXY L Q L + lXY R u R +mY L Y R – l is O(1) with this scenario, GLAST could probe for halo density J ~ 3, l ~ 0.3 –this is the lower end of what various theories predict –most dark matter models do not allow one to probe this region

Direct Detection limits need to see if this is ruled out by direct detection bounds DM passing through earthbound detector transfers momentum to nucleus via elastic scattering expect not bounded –direct detection sensitivity scales with number density –goes bad ~ 10 GeV can compute direct detection limits –for l and M X in our range, not ruled out by direct detection note, could have coupled to t instead of up-quark –then indirect detection sensitivity is basically the same –but no direct detection possibility Dan Hooper SUSY ‘07

Conclusion string theory can be a powerful generator of ideas for new physics –the tight constraints of consistent quantum gravity can illustrate new scenarios and features which otherwise would be less noticed phenomenology, collider physics, cosmology –ideas aren’t exclusive to string theory (and thus neither prove nor falsify), but the question is if they satisfy the “usefulness” test much more to learn ….