Abstract
We consider SU(N ) mathcal{N} = 4 super Yang-Mills with cubic and quadratic soft SUSY breaking potential, such that the global SU(4)R is broken to SU(3) or further. As shown recently, this set-up supports a rich set of non-trivial vacua with the geometry of self-intersecting SU(3) branes in 6 extra dimensions. The zero modes on these branes can be interpreted as 3 generations of bosonic and chiral fermionic strings connecting the branes at their intersections. Here, we uncover a large class of exact solutions consisting of branes connected by Higgs condensates, leading to Yukawa couplings between the chiral fermionic zero modes. Under certain decoupling conditions, the backreaction of the Higgs on the branes vanishes exactly. The resulting physics is that of a spontaneously broken chiral gauge theory on branes with fluxes. In particular, we identify combined brane plus Higgs configurations which lead to gauge fields that couple to chiral fermions at low energy. This turns out to be quite close to the Standard Model and its constructions via branes in string theory. As a by-product, we construct a G2-brane solution corresponding to a squashed fuzzy coadjoint orbit of G2.
Highlights
IntroductionDeformed or softly broken versions of N = 4 super Yang-Mills (SYM), for example via extra terms in the potential, may lead to more interesting vacua and low-energy physics
Among all 4-dimensional supersymmetric gauge theories, N = 4 super Yang-Mills (SYM) is the most special and rigid model
The IKKT matrix model on noncommutative D3-brane solutions reduces to the U(N ) N = 4 SYM [21], where space-time and fuzzy extra dimensions are treated on the samen footing
Summary
Deformed or softly broken versions of N = 4 SYM, for example via extra terms in the potential, may lead to more interesting vacua and low-energy physics It is well-known that certain mass-deformations to the superpotential, which preserve N = 1, have a much richer vacuum structure [7,8,9,10,11,12], including stacks of fuzzy spheres which partially or completely break the gauge symmetry. Adding suitable soft SUSY breaking terms to the potential can lead to vacua with even richer geometries, including S2 × S2 [16,17,18,19], S4 [20], and others This generation of fuzzy extra dimensions is interesting from the matrix model point of view. We focus, on the familiar gauge theory setting on R3,1
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