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M Theory, Type IIA String and 4D N=1 SUSY SU(N_L) X SU(N_R) Gauge Theory

Amit Giveon, Oskar Pelc

Abstract

SU(N_L) X SU(N_R) gauge theories are investigated as effective field theories on D_4 branes in type IIA string theory. The classical gauge configuration is shown to match quantitatively with a corresponding classical U(N_L) X U(N_R) gauge theory. Quantum effects freeze the U(1) gauge factors and turn some parameters into moduli. The SU(N_L) X SU(N_R) quantum model is realized in M theory. Starting with an N=2 configuration (parallel NS fivebranes), the rotation of a single NS fivebrane is considered. Generically this leads to a complete lifting of the Coulomb moduli space. The implications of this result to field theory and the dynamics of branes are discussed. When the initial M fivebrane is reducible, part of the Coulomb branch may survive. Some such situations are considered, leading to curves describing the effective gauge couplings for N=1 models. The generalization to models with more gauge group factors is also discussed.

M Theory, Type IIA String and 4D N=1 SUSY SU(N_L) X SU(N_R) Gauge Theory

Abstract

SU(N_L) X SU(N_R) gauge theories are investigated as effective field theories on D_4 branes in type IIA string theory. The classical gauge configuration is shown to match quantitatively with a corresponding classical U(N_L) X U(N_R) gauge theory. Quantum effects freeze the U(1) gauge factors and turn some parameters into moduli. The SU(N_L) X SU(N_R) quantum model is realized in M theory. Starting with an N=2 configuration (parallel NS fivebranes), the rotation of a single NS fivebrane is considered. Generically this leads to a complete lifting of the Coulomb moduli space. The implications of this result to field theory and the dynamics of branes are discussed. When the initial M fivebrane is reducible, part of the Coulomb branch may survive. Some such situations are considered, leading to curves describing the effective gauge couplings for N=1 models. The generalization to models with more gauge group factors is also discussed.

Paper Structure

This paper contains 28 sections, 90 equations, 3 figures.

Table of Contents

  1. The Classical $U(N_L)\times U(N_R)$ Model
  2. $\mu_L\mu_R=0$
  3. $\mu_L\mu_R\neq0$
  4. The Classical $SU(N_L)\otimes SU(N_R)$ Model
  5. $\mu_L=\mu_R=0$
  6. $\mu_L\neq0=\mu_R$
  7. $\mu_L\mu_R\neq0$
  8. The Quantum $SU(N_L)\otimes SU(N_R)$ Model
  9. $\mu_L=\mu_R=0$
  10. $N_L=N_R:=N$, $\mu_L=-\mu_R:=-\mu\neq0$
  11. $\mu_L\neq0=\mu_R$
  12. The Classical Description
  13. Identification of the Effective Field Theory
  14. Quantum effects
  15. The Bending of $N\space S_5$ Branes
  16. ...and 13 more sections

Figures (3)

  • Figure 1: Projection on the $(v,s)$ subspace. For brevity, only one $D_4$ brane is displayed in each region; the displacements are the eigenvalues of the corresponding matrices ($m_L,A_L,A_R,m_R$).
  • Figure 2: Projection on the $(v,w)$ subspace. The displacements described are for an $S_L\leftrightarrow S_R$$D_4$ brane (denoted by a bullet $\bullet$).
  • Figure 3: The possible brane configurations. The types of configurations correspond to the types of vacua found in section \ref{['FT']}.