Related papers: $SU(n)$ symmetry breaking by rank three and rank t…
We present a dual description for $SU(N)$ supersymmetric gauge theory with an antisymmetric tensor and fundamentals, and no superpotential. This duality is derived from the dualities of Seiberg. Under a perturbation of the superpotential,…
The N=1 supersymmetric gauge SU(5) theory with one antisymmetric tensor, n+3 fundamentals and n+4 antifundamentals has dual magnetic descriptions in the infrared. By introducing extra singlet fields and tree level superpotential terms to…
Working with explicit examples given by the 56 representation in $SU(8)$, and the 10 representation in $SU(5)$, we show that symmetry breaking of a group ${\cal G}\supset {\cal G}_1 \times {\cal G}_2$ by a scalar in a rank three or two…
We study $SU(8)$ symmetry breaking induced by minimizing the Coleman-Weinberg effective potential for a third rank antisymmetric tensor scalar field in the 56 representation. Instead of breaking $SU(8) \supset SU(3) \times SU(5)$, we find…
We study dynanics of $SU(N-4)$ gauge theories with fermions in rank-2 symmetric tensor and $N$ anti-fundamental representations, by perturbing supersymmetric theories with anomaly-mediated supersymmetry breaking. We find the $SU(N)\times…
We study the symmetric tensor rank of multiplication over finite field extensions using linearized polynomials. Via field trace, symmetric linearized polynomials are identified with symmetric bilinear forms and symmetric matrices, allowing…
We lower bound the rank of a tensor by a linear combination of the ranks of three of its unfoldings, using Sylvester's rank inequality. In a similar way, we lower bound the symmetric rank by a linear combination of the symmetric ranks of…
We analyze to all perturbative orders the properties of two possible quantum extensions of classically on-shell equivalent antisymmetric tensor gauge models in four dimensions. The first case, related to the soft breaking of a topological…
We investigate three classes of supersymmetric models which can be obtained by breaking the chiral SU(2k+3) gauge theories with one antisymmetric tensor and 2k-1 antifundamentals. For N=3, the chiral SU(2k)$\times$SU(3)$\times$U(1) theories…
We study a set of theories built on a ranked sequence of antisymmetric tensor fields in D dimensional space-time. These linear theories exhibit gauge invariances that are analogous to the local gauge invariance of a massless vector…
This thesis focuses on renormalization of quantum field theories. Its first part considers three tensor models in three dimensions, a Fermionic quartic with tensors of rank-3 and two Bosonic sextic, of ranks 3 and 5. We rely upon the…
A symmetric tensor may be regarded as a partially symmetric tensor in several different ways. These produce different notions of rank for the symmetric tensor which are related by chains of inequalities. By exploiting algebraic tools such…
This paper is a manual with tips and tricks for programming tensor network algorithms with global $SU(2)$ symmetry. We focus on practical details that are many times overlooked when it comes to implementing the basic building blocks of…
In this work we consider the issue of localization of antisymmetric tensor fields of arbitrary rank in a D dimensional Space-time with a codimension two. A string-like defect is used to simulate the membrane. The localization of massless…
Radiatively induced SU(2) symmetry breaking is shown to be a genuine feature of SU(2) x O(N) globally symmetric renormalisable field theories in the large N limit, describing interaction of a complex SU(2) doublet, O(N)-singlet field with…
In this note, we consider the highly nonconvex optimization problem associated with computing the rank decomposition of symmetric tensors. We formulate the invariance properties of the loss function and show that critical points detected by…
We study a $SU(2)$-symmetric spin-${3}/{2}$ system on a bipartite lattice close to the antiferromagnetic $SU(4)$-symmetric point, which can be described by the $CP^{3}$ model with a perturbation breaking the symmetry from $SU(4)$ down to…
Within the framework of the functional renormalization group, we derived the flow equations for the scale-dependent effective action at finite temperature for models involving an antisymmetric rank-2 tensor field. The analysis focuses on…
Consequences of explicit symmetry breaking in a physically motivated model of SU(N) antiferromagnet in spatial dimensions one and two are studied. It is shown that the case N=3, which can be realized in spin-1 cold atom systems, displays…
We discuss an embedding of $su(n)$ rank-two antisymmetric supercharges in the $su(2,2|d_n)$ superalgebra, where $d_n=n(n-1)/2$. We describe an algorithm to construct the explicit form of the generators of the superalgebra.