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Register a new userEnhanced Worldvolume Supersymmetry and Intersecting Domain Walls in N=1 SQCD
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We study the worldvolume dynamics of BPS domain walls in N=1 SQCD with N_f=N flavors, and exhibit an enhancement of supersymmetry for the reduced moduli space associated with broken flavor symmetries. We provide an explicit construction of the worldvolume superalgebra which corresponds to an N=2 Kahler sigma model in 2+1D deformed by a potential, given by the norm squared of a U(1) Killing vector, resulting from the flavor symmetries broken by unequal quark masses. This framework leads to a worldvolume description of novel two-wall junction configurations, which are 1/4-BPS objects, but nonetheless preserve two supercharges when viewed as kinks on the wall worldvolume.
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We consider supersymmetric domain walls of four-dimensional $mathcal{N}!=!1$ $Sp(N)$ SQCD with $F!=!N+1$ and $F!=!N+2$ flavors. First, we study numerically the differential equations defining the walls, classifying the solutions. When $F!=!N+2$, in the special case of the parity-invariant walls, the naive analysis does not provide all the expected solutions. We show that an infinitesimal deformation of the differential equations sheds some light on this issue. Second, we discuss the $3d$ $mathcal{N}!=!1$ Chern-Simons-matter theories that should describe the effective dynamics on the walls. These proposals pass various tests, including dualities and matching of the vacua of the massive $3d$ theory with the $4d$ analysis. However, for $F!=!N+2$, the semiclassical analysis of the vacua is only partially successful, suggesting that yet-to-be-understood strong coupling phenomena are into play in our $3d$ $mathcal{N}!=!1$ gauge theories.
We study supersymmetric domain walls of four dimensional $SU(N)$ SQCD with $N$ and $N+1$ flavors. In $4d$ we analyze the BPS differential equations numerically. In $3d$ we propose the $mathcal{N}=1$ Chern-Simons-Matter gauge theories living on the walls. Compared with the previously studied regime of $F<N$ flavors, we encounter a couple of novelties: with $N$ flavors, there are solutions/vacua breaking the $U(1)$ baryonic symmetry; with $N+1$ flavors, our $3d$ proposal includes a linear monopole operator in the superpotential.
Coincident D3-branes placed at a conical singularity are related to string theory on $AdS_5times X_5$, for a suitable five-dimensional Einstein manifold $X_5$. For the example of the conifold, which leads to $X_5=T^{1,1}=(SU(2)times SU(2))/U(1)$, the infrared limit of the theory on $N$ D3-branes was constructed recently. This is ${cal N}=1$ supersymmetric $SU(N)times SU(N)$ gauge theory coupled to four bifundamental chiral superfields and supplemented by a quartic superpotential which becomes marginal in the infrared. In this paper we consider D3-branes wrapped over the 3-cycles of $T^{1,1}$ and identify them with baryon-like chiral operators built out of products of $N$ chiral superfields. The supergravity calculation of the dimensions of such operators agrees with field theory. We also study the D5-brane wrapped over a 2-cycle of $T^{1,1}$, which acts as a domain wall in $AdS_5$. We argue that upon crossing it the gauge group changes to $SU(N)times SU(N+1)$. This suggests a construction of supergravity duals of ${cal N}=1$ supersymmetric $SU(N_1)times SU(N_2)$ gauge theories.
We discuss the special holonomy metrics of Gibbons, Lu, Pope and Stelle, which were constructed as nilmanifold bundles over a line by uplifting supersymmetric domain wall solutions of supergravity to 11 dimensions. We show that these are dual to intersecting brane solutions, and considering these leads us to a more general class of special holonomy metrics. Further dualities relate these to non-geometric backgrounds involving intersections of branes and exotic branes. We discuss the possibility of resolving these spaces to give smooth special holonomy manifolds.
We study the multiplicity of BPS domain walls in N=1 super Yang-Mills theory, by passing to a weakly coupled Higgs phase through the addition of fundamental matter. The number of domain walls connecting two specified vacuum states is then determined via the Witten index of the induced worldvolume theory, which is invariant under the deformation to the Higgs phase. The worldvolume theory is a sigma model with a Grassmanian target space which arises as the coset associated with the global symmetries broken by the wall solution. Imposing a suitable infrared regulator, the result is found to agree with recent work of Acharya and Vafa in which the walls were realized as wrapped D4-branes in IIA string theory.
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