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Deformed Intersecting D6-Brane GUTS I

Christos Kokorelis

TL;DR

This work constructs four-stack D6-brane realizations of Pati–Salam GUTs in type IIA with intersecting branes, achieving exactly the Standard Model spectrum at low energy while maintaining proton stability through a gauged baryon number. Extra U(1) branes are employed to satisfy RR tadpole cancellation, generating singlet scalars and enabling breaking of residual U(1) factors via SUSY-induced sectors and a Green–Schwarz mechanism. Neutrino masses arise from a see-saw structure with Majorana couplings, and a natural $m_e=m_d$ relation emerges at the GUT scale; the model also accommodates light electroweak doublets and a potentially low string scale. Tachyon-free consistency requires a set of angle inequalities, with moduli fixing through SUSY conditions on specific sectors. Overall, the PS-I class offers a testable, UV-complete brane-world route to SM-like physics with distinctive signatures at colliders and in neutrino sectors.

Abstract

By employing D6-branes intersecting at angles in $D = 4$ type IIA strings, we construct {\em four stack string GUT models} (PS-I class), that contain at low energy {\em exactly the three generation Standard model} with no extra matter and/or extra gauge group factors. These classes of models are based on the Pati-Salam (PS) gauge group $SU(4)_C \times SU(2)_L \times SU(2)_R$. They represent deformations around the quark and lepton basic intersection number structure. The models possess the same phenomenological characteristics of some recently discussed examples (PS-A class) of four stack PS GUTS. Namely, there are no colour triplet couplings to mediate proton decay and proton is stable as baryon number is a gauged symmetry. Neutrinos get masses of the correct sizes. Also the mass relation $m_e = m_d$ at the GUT scale is recovered. Moreover, we clarify the novel role of {\em extra} branes, the latter having non-trivial intersection numbers with quarks and leptons and creating scalar singlets, needed for the satisfaction of RR tadpole cancellation conditions. The presence of N=1 supersymmetry in sectors involving the {\em extra} branes is equivalent to the, model dependent, orthogonality conditions of the U(1)'s surviving massless the generalized Green-Schwarz mechanism. The use of {\em extra} branes creates mass couplings that predict the appearance of light fermion doublets up to the scale of electroweak scale symmetry breaking.

Deformed Intersecting D6-Brane GUTS I

TL;DR

This work constructs four-stack D6-brane realizations of Pati–Salam GUTs in type IIA with intersecting branes, achieving exactly the Standard Model spectrum at low energy while maintaining proton stability through a gauged baryon number. Extra U(1) branes are employed to satisfy RR tadpole cancellation, generating singlet scalars and enabling breaking of residual U(1) factors via SUSY-induced sectors and a Green–Schwarz mechanism. Neutrino masses arise from a see-saw structure with Majorana couplings, and a natural relation emerges at the GUT scale; the model also accommodates light electroweak doublets and a potentially low string scale. Tachyon-free consistency requires a set of angle inequalities, with moduli fixing through SUSY conditions on specific sectors. Overall, the PS-I class offers a testable, UV-complete brane-world route to SM-like physics with distinctive signatures at colliders and in neutrino sectors.

Abstract

By employing D6-branes intersecting at angles in type IIA strings, we construct {\em four stack string GUT models} (PS-I class), that contain at low energy {\em exactly the three generation Standard model} with no extra matter and/or extra gauge group factors. These classes of models are based on the Pati-Salam (PS) gauge group . They represent deformations around the quark and lepton basic intersection number structure. The models possess the same phenomenological characteristics of some recently discussed examples (PS-A class) of four stack PS GUTS. Namely, there are no colour triplet couplings to mediate proton decay and proton is stable as baryon number is a gauged symmetry. Neutrinos get masses of the correct sizes. Also the mass relation at the GUT scale is recovered. Moreover, we clarify the novel role of {\em extra} branes, the latter having non-trivial intersection numbers with quarks and leptons and creating scalar singlets, needed for the satisfaction of RR tadpole cancellation conditions. The presence of N=1 supersymmetry in sectors involving the {\em extra} branes is equivalent to the, model dependent, orthogonality conditions of the U(1)'s surviving massless the generalized Green-Schwarz mechanism. The use of {\em extra} branes creates mass couplings that predict the appearance of light fermion doublets up to the scale of electroweak scale symmetry breaking.

Paper Structure

This paper contains 13 sections, 99 equations, 1 figure, 8 tables.

Table of Contents

  1. Introduction
  2. Model structure and the rules of computing the spectrum
  3. The basic fermion structure
  4. Extra brane engineering - the case of PS-A class of models
  5. Tadpole cancellation for the PS-I models
  6. Cancellation of U(1) Anomalies
  7. Higgs sector, $N=1$ SUSY on intersections and extra U(1)'s
  8. Stability of the configurations and Higgs sector
  9. $N=1$ SUSY on Intersections
  10. Breaking the extra U(1)'s
  11. Neutrino couplings and fermion masses
  12. Conclusions
  13. Tachyon free conditions for classes of PS-I GUTS

Figures (1)

  • Figure 1: Assignment of angles between D6-branes on a a type I PS-I class of models based on the initial gauge group $U(4)_C\times {U(2)}_L\times {U(2)}_R$. The angles between branes are shown on a product of $T^2 \times T^2 \times T^2$. We have chosen $\beta_1 =1$, $m_b^1, m_c^1, n_a^2 >0$, $\epsilon = {\tilde{\epsilon}}= 1$. These models break to low energies to exactly the SM.