# Can large N{sub c} equivalence between supersymmetric Yang-Mills theory and its orbifold projections be valid?

## Abstract

In previous work, we found that necessary and sufficient conditions for large N{sub c} equivalence between parent and daughter theories, for a wide class of orbifold projections of U(N{sub c}) gauge theories, are just the natural requirements that the discrete symmetry used to define the projection not be spontaneously broken in the parent theory, and the discrete symmetry permuting equivalent gauge group factors not be spontaneously broken in the daughter theory. In this paper, we discuss the application of this result to Z{sub k} projections of N=1 supersymmetric Yang-Mills theory in four dimensions, as well as various multiflavor generalizations. Z{sub k} projections with k>2 yielding chiral gauge theories violate the symmetry realization conditions needed for large N{sub c} equivalence, due to the spontaneous symmetry breaking of discrete chiral symmetry in the parent super-Yang-Mills theory. But for Z{sub 2} projections, we show that previous assertions of large N{sub c} inequivalence, in infinite volume, between the parent and daughter theories were based on incorrect mappings of vacuum energies, theta angles, or connected correlators between the two theories. With the correct identifications, there is no sign of any inconsistency. A subtle but essential feature of the connection between parent and daughter theories involvesmore »

- Authors:

- KITP, University of California, Santa Barbara, California 93106 (United States)
- Department of Physics, Boston University, Boston, Massachusetts 02215 (United States)
- Department of Physics, University of Washington, Seattle, Washington 98195-1560 (United States)

- Publication Date:

- OSTI Identifier:
- 20711585

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 72; Journal Issue: 10; Other Information: DOI: 10.1103/PhysRevD.72.105006; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CHIRAL SYMMETRY; CHIRALITY; GAUGE INVARIANCE; QUANTUM FIELD THEORY; SUPERSYMMETRY; SYMMETRY BREAKING; U GROUPS; UNITARY SYMMETRY; VACUUM STATES; YANG-MILLS THEORY

### Citation Formats

```
Kovtun, Pavel, Uensal, Mithat, and Yaffe, Laurence G.
```*Can large N{sub c} equivalence between supersymmetric Yang-Mills theory and its orbifold projections be valid?*. United States: N. p., 2005.
Web. doi:10.1103/PhysRevD.72.105006.

```
Kovtun, Pavel, Uensal, Mithat, & Yaffe, Laurence G.
```*Can large N{sub c} equivalence between supersymmetric Yang-Mills theory and its orbifold projections be valid?*. United States. doi:10.1103/PhysRevD.72.105006.

```
Kovtun, Pavel, Uensal, Mithat, and Yaffe, Laurence G. Tue .
"Can large N{sub c} equivalence between supersymmetric Yang-Mills theory and its orbifold projections be valid?". United States.
doi:10.1103/PhysRevD.72.105006.
```

```
@article{osti_20711585,
```

title = {Can large N{sub c} equivalence between supersymmetric Yang-Mills theory and its orbifold projections be valid?},

author = {Kovtun, Pavel and Uensal, Mithat and Yaffe, Laurence G.},

abstractNote = {In previous work, we found that necessary and sufficient conditions for large N{sub c} equivalence between parent and daughter theories, for a wide class of orbifold projections of U(N{sub c}) gauge theories, are just the natural requirements that the discrete symmetry used to define the projection not be spontaneously broken in the parent theory, and the discrete symmetry permuting equivalent gauge group factors not be spontaneously broken in the daughter theory. In this paper, we discuss the application of this result to Z{sub k} projections of N=1 supersymmetric Yang-Mills theory in four dimensions, as well as various multiflavor generalizations. Z{sub k} projections with k>2 yielding chiral gauge theories violate the symmetry realization conditions needed for large N{sub c} equivalence, due to the spontaneous symmetry breaking of discrete chiral symmetry in the parent super-Yang-Mills theory. But for Z{sub 2} projections, we show that previous assertions of large N{sub c} inequivalence, in infinite volume, between the parent and daughter theories were based on incorrect mappings of vacuum energies, theta angles, or connected correlators between the two theories. With the correct identifications, there is no sign of any inconsistency. A subtle but essential feature of the connection between parent and daughter theories involves multivaluedness in the mapping of theta parameters from parent to daughter.},

doi = {10.1103/PhysRevD.72.105006},

journal = {Physical Review. D, Particles Fields},

number = 10,

volume = 72,

place = {United States},

year = {Tue Nov 15 00:00:00 EST 2005},

month = {Tue Nov 15 00:00:00 EST 2005}

}