PHENOMENOLOGY OF HETEROTIC AND TYPE II ORIENTIFOLD STRING MODELS A Dissertation by VAN ERIC MAYES Submitted to the O±ce of Graduate Studies of Texas A&M University in partial ful¯llment of the requirements for the degree of DOCTOR OF PHILOSOPHY August 2007 Major Subject: Physics PHENOMENOLOGY OF HETEROTIC AND TYPE II ORIENTIFOLD STRING MODELS A Dissertation by VAN ERIC MAYES Submitted to the O±ce of Graduate Studies of Texas A&M University in partial ful¯llment of the requirements for the degree of DOCTOR OF PHILOSOPHY Approved by: Chair of Committee, Dimitri Nanopoulos Committee Members, Richard Arnowitt Christopher Pope Stephen Fulling Head of Department, Edward Fry August 2007 Major Subject: Physics iii ABSTRACT Phenomenology of Heterotic and Type II Orientifold String Models. (August 2007) Van Eric Mayes, B.S., Texas A&M University; M.S., Texas A&M University Chair of Advisory Committee: Dr. Dimitri Nanopoulos Cryptons are metastable bound states of fractionally-charged particles that arise generically in the hidden sectors of models derived from heterotic string. We study their properties and decay modes in a speci¯c flipped SU(5) model with long-lived four-particle spin-zero bound states called tetrons. The expected masses and lifetimes of the neutral tetrons make them good candidates for cold dark matter (CDM), and a potential source of the ultra-high energy cosmic rays (UHECRs) which have been observed, whereas the charged tetrons would have decayed in the early Universe. We calculate the spectra of ultra-high-energy cosmic rays (UHECRs) in an ex- plicit top-down model based on the decays of metastable neutral `crypton' states. For all the decay operators, the total UHECR spectra are compatible with the available data. Also, the fractions of photons are compatible with all the published upper limits, but may be detectable in future experiments. We also construct several intersecting D-brane models on a variety of orientifold backgrounds. In particular, we construct flipped SU(5), Pati-Salam, and MSSM-like models. The phenomenological properties of these models are studied. For one model in particular, we ¯nd that we may explain the quark masses and mixings, the tau lepton mass, and generate small neutrino masses via the see-saw mechanism. iv To my family and friends. v ACKNOWLEDGMENTS I would ¯rst like to acknowledge my Ph.D. advisor, Dr. Dimitri Nanopoulos, who taught me almost everything I know about particle physics and string theory. I would also like to acknowledge John Ellis, with whom I wrote my ¯rst two papers on theoretical physics and from whom I learned a great deal. I would also like to thank all the members of my doctoral committee for being willing to serve. I cannot overlook the assistance of Ching-Ming Chen, George Kraniotis, and Tianjun Li with whom I had many productive collaborations. vi TABLE OF CONTENTS CHAPTER Page I INTRODUCTION :::::::::::::::::::::::::: 1 A. Cryptons and Ultra-High Energy Cosmic Rays . 6 B. Intersecting D-branes . 8 II FLIPPED CRYPTONS AND UHECRS :::::::::::::: 12 A. Introduction . 12 B. Field and Particle Content in the Flipped SU(5) Model . 14 C. Crypton Bound States . 20 D. The Decays of the Lightest SU(4) Mesons . 22 E. The Fate of the Neutral Tetrons . 24 F. The Fate of the Charged Tetrons . 26 G. Generic Super-heavy Relic Decay . 29 III A SUPERSYMMETRIC FLIPPED SU(5) INTERSECTING BRANE WORLD :::::::::::::::::::::::::: 45 A. Introduction . 45 B. Search for Supersymmetric Flipped SU(5)£U(1)X Brane 6 Models on a T =(Z2 £ Z2) Orientifold . 49 1. RR-tadpole Consistency Conditions . 51 2. Conditions for Supersymmetric Brane Con¯gurations . 52 3. Intersection Numbers . 53 4. Generalized Green-Schwarz Mechanism . 54 C. Flipped SU(5) £ U(1)X Model Building . 55 1. Basic Flipped SU(5) Phenomenology . 55 2. Model Building . 57 IV FLIPPED SU(5) FROM D-BRANES WITH TYPE IIB FLUXES 63 A. Introduction . 63 6 B. D-branes with Type IIB Flux on the T =(Z2 £ Z2) Orientifold 67 1. Magnetized D-branes in Type IIB Theory . 67 2. The Fermionic Spectrum . 69 3. Turning on Type IIB Fluxes . 70 4. Supersymmetry Conditions . 71 vii CHAPTER Page a. Supersymmetry Conditions in the Closed String Sector . 71 b. Supersymmetry Conditions in the Open String Sector . 73 5. RR Tadpole Cancellation and K-theory Constraints . 73 6. The Green-Schwarz Mechanism for Flipped SU(5) GUT Construction . 75 C. Flipped SU(5) £ U(1)X Model Building . 76 1. Basic Flipped SU(5) Phenomenology . 76 D. Some Models with Fluxes . 78 1. Nflux = 192 . 78 2. Nflux = 128 . 79 3. Nflux = 1 £ 64 . 79 V MSSM VIA PATI-SALAM FROM INTERSECTING BRANES 6 0 ON T =(Z2 £ Z2) :::::::::::::::::::::::::: 83 A. Introduction . 83 B. Intersecting Branes on the Z2 £Z2 Orientifold with and without Discrete Torsion . 85 C. Consistency and SUSY conditions . 90 1. RR and Torsion Charge Cancellation . 90 2. Conditions for Preserving N = 1 Supersymmetry . 92 3. The Green-Schwarz Mechanism . 93 4. K-Theory Constraints . 96 D. MSSM via Pati-Salam . 96 E. Gauge Coupling Uni¯cation . 105 VI CONCLUSIONS ::::::::::::::::::::::::::: 107 REFERENCES ::::::::::::::::::::::::::::::::::: 112 VITA :::::::::::::::::::::::::::::::::::::::: 124 viii LIST OF TABLES TABLE Page I Net chiral matter spectrum in terms of the three-cycles de¯ned on the orbifold space. :::::::::::::::::::::::::: 9 II Charges and hypercharges for crypton ¯elds in flipped SU(5). :::: 18 III Wrapping numbers and their consistent parameters. :::::::::: 61 IV List of intersection numbers. The number in parenthesis indicates the multiplicity of non-chiral pairs. ::::::::::::::::::: 61 6 V The spectrum of U(5) £ U(1) £ Usp(2), or SU(5) £ U(1)X £ U(1)Y £ U(1)Z £ Usp(2), with the four global U(1)s from the Green-Schwarz mechanism. The ?0d representations indicate vector-like non-chiral pairs. : 62 VI Spectrum of bi-fundamental representations. :::::::::::::: 69 VII List of wrapping numbers and intersection numbers for three- fluxes Nflux = 192. The number in parenthesis indicates the multiplicity of non-chiral pairs. Here xA = 62, xB = 1, xC = 1, and xD = 2. Clearly, the ¯rst K-theory constraint is not satis¯ed. :: 78 VIII Nflux = 128. The number stacks is only two plus two ¯ller branes, though it has very few exotic particles, we have too few stacks to complete the cancellation of U(1)X mass. Here xA = 27, xB = 1, xC = 1, and xD = 2. ::::::::::::::::::::::::::: 79 IX List of intersection numbers for Nflux = 64 with gauge group U(5)£U(1)5. The number in parenthesis indicates the multiplicity of non-chiral pairs. :::::::::::::::::::::::::::: 79 5 X The spectrum of U(5) £ U(1) , or SU(5) £ U(1)X £ U(1)Y , with the four global U(1)s from the Green-Schwarz mechanism. The ?0d representations indicate vector-like matter. We list the two cases for the U(1)Y . ::::::::::::::::::::::::::: 82 ix TABLE Page XI Net chiral matter spectrum in terms of three-cycles. :::::::::: 90 XII Stacks, wrapping numbers, and torsion charges for a Pati-Salam p model. With the choice of structure parameters x = 3; x = p a b xc = xd = 3=3, N = 1 SUSY will be preserved. The cycles pass through the same set of ¯xed points for each stack. :::::::::: 97 XIII Intersection numbers between di®erent stacks giving rise to fermions in the bifundamental representation. The result is a four-generation Pati-Salam model. :::::::::::::::::::::::::::: 97 XIV Intersection numbers between di®erent stacks and their images giving rise to antisymmetric and symmetric representations for a Pati-Salam model. :::::::::::::::::::::::::::: 98 4 XV The `observable' spectrum of SU(4)£SU(2)L £SU(2)R £[U(2) £ U(1)3]. The ?0d representations indicate light, non-chiral matter which is present between pairs of fractional branes which wrap homologically identical bulk cycles, but di®er in their twisted cycles. 98 XVI Stacks, wrapping numbers, and torsion charges for an MSSM-like model. The cycles pass through the same set of ¯xed points for each stack. :::::::::::::::::::::::::::::::: 100 XVII Intersection numbers between di®erent stacks giving rise to fermions in the bifundamental representation. The result is a four-generation MSSM-like model. :::::::::::::::::::::::::::: 101 XVIII Intersersection numbers between di®erent stacks and their images giving rise to antisymmetric and symmetric representations for an MSSM-like model. :::::::::::::::::::::::::::: 101 4 XIX The `observable' spectrum of [SU(3) £ SU(2)L £ U(1)Y ]£U(2) £ U(1)4. The ?0d representations indicate light, non-chiral matter which exist between pairs of fractional branes which wrap identical bulk cycles, but di®er in their twisted cycles. ::::::::::::: 102 x LIST OF FIGURES FIGURE Page 1 The top panel shows the total UHECR spectrum and the bottom 0 c 3 panel the photon fraction for the decay mode ª ! s s hd Á . :::: 36 2 The top panel shows the total UHECR spectrum and the bottom panel the photon fraction for the decay mode ª0 ! c cc d dc Á2. ::: 37 3 The top panel shows the total UHECR spectrum and the bottom panel 0 c 3 the photon fraction for the decay mode ª ! b b hd Á . ::::::::: 38 4 The top panel shows the total UHECR spectrum and the bottom 0 c panel the photon fraction for the decay mode ª ! b b hd hd huÁ. : 39 5 The top panel shows the total UHECR spectrum and the bottom panel 0 c 3 the photon fraction for the decay mode ª ! t t hu Á . ::::::::: 40 6 The top panel shows the total UHECR spectrum and the bottom 0 c panel the photon fraction for the decay mode ª ! t t hu hu hd Á. : 41 7 The top panel shows the total UHECR spectrum and the bottom 0 c c 3 panel the photon fraction for the decay mode ª ! e=¹ e =¹ hd Á .