The analysis of spontaneous gauge symmetry breaking of N=1 supersymmetric SU(N_c) Yang-Mills theory with matter is performed. The supersymmetric $R_ξ$-gauge is used and its non-local effects investigated. Superpropagators and vertices are computed, and it is shown that the non-local terms introduced by the $R_ξ$-gauge-fixing are well-behaved in general gauge at one-loop. It is argued that this feature generalizes to multiple loops.
Supergravities with gauged R-symmetry and Minkowski vacua allow for spontaneous supersymmetry breaking and, as such, provide a framework for building supergravity models of phenomenological relevance. In this letter we initiate the study of double-copy constructions for these supergravities. We argue that, on general grounds, we expect their scattering amplitudes to be described by a double copy of the type: (Higgsed gauge theory) x (gauge theory with broken SUSY). We present a simple realization in which the resulting supergravity has U(1)_R gauge symmetry, spontaneously-broken N=2 supersymme…
这些是在巴黎“Gif 2000”暑期学校所作的讲座的扩充笔记。它们构成了“超对称性和超引力导论”的第一部分，第二部分由J. P. Derendinger很快就会出现。本导言是初步的、务实的。我讨论：旋量和庞加莱群，susy代数和susy多重态，超场和susy拉格朗日量，susy规范理论，自发破缺susy，非线性西格玛模型，N=2 susy规范理论，最后是塞伯格-威滕对偶。
Quantum field theories with exact but spontaneously broken conformal invariance have an intriguing feature: their vacuum energy (cosmological constant) is equal to zero. Up to now, the only known ultraviolet complete theories where conformal symmetry can be spontaneously broken were associated with supersymmetry (SUSY), with the most prominent example being the $\mathcal N$=4 SUSY Yang-Mills. In this Letter we show that the recently proposed conformal "fishnet" theory supports at the classical level a rich set of flat directions (moduli) along which conformal symmetry is spontaneously broken. …
In this work, we adopt the simplest model that spontaneously breaks supersymmetry, namely, the minimal O'Raifeartaigh model. The effective potential is computed in the framework of the linear delta expansion (LDE) approach up to the order $δ^2$, conjugated with superspace and supergraph techniques. The latter can be duly mastered even if supersymmetry is no longer exact and the efficacy of the superfield approach in connection with the LDE procedure is confirmed according to our investigation. That opens up a way for a semi-nonperturbative superspace computation which allows us to deal with sp…
We study the quantum mechanical sigma model arising in the discrete light-cone quantisation of N=4 supersymmetric Yang-Mills theory. The target space is a certain torus fibration over a scale-invariant special Kahler manifold. We show that the expected SU(1,1|4) light-cone superconformal invariance of the N=4 theory emerges in a limit where the volume of the fibre goes to zero and give an explicit construction of the generators. The construction given here yields a large new family of superconformal quantum mechanical models with SU(1,1|4) invariance.
The simplest gauge theories for the conservation of R-parity in supersymmetry are discussed. We show how the minimal theory based on the B-L gauge symmetry predicts that R-parity must be spontaneously broken at the TeV scale. The most striking signals of these theories at the Large Hadron Collider are discussed. We present a realistic theory where the local baryon and lepton numbers are spontaneously broken at the supersymmetry breaking scale. The possibility to understand the conservation of R-parity in grand unified theories defined in four dimensions is mentioned.
We present a conjecture for the normalisation of the twist two conformal partial waves in a double OPE limit of the four-point function of stress tensor multiplets in N = 4 super Yang-Mills theory up to three loops. This contains information about the structure constants in the OPE. Like the twist two anomalous dimensions our result is expressed as a linear combination of harmonic sums whose argument is the spin of the exchanged operators. To arrive at the result we derive asymptotic expansions for the twist two part of two unknown three-loop integrals using the method of expansion by regions,…
Color/kinematics duality and the double-copy construction have proved to be systematic tools for gaining new insight into gravitational theories. Extending our earlier work, in this paper we introduce new double-copy constructions for large classes of spontaneously-broken Yang-Mills-Einstein theories with adjoint Higgs fields. One gauge-theory copy entering the construction is a spontaneously-broken (super-)Yang-Mills theory, while the other copy is a bosonic Yang-Mills-scalar theory with trilinear scalar interactions that display an explicitly-broken global symmetry. We show that the kinemati…
We consider a U(2) Yang-Mills theory on M x S_F^2 where M is an arbitrary noncommutative manifold and S_F^2 is a fuzzy sphere spontaneously generated from a noncommutative U(N) Yang-Mills theory on M, coupled to a triplet of scalars in the adjoint of U(N). Employing the SU(2)-equivariant gauge field constructed in arXiv:0905.2338, we perform the dimensional reduction of the theory over the fuzzy sphere. The emergent model is a noncommutative U(1) gauge theory coupled adjointly to a set of scalar fields. We study this model on the Groenewald-Moyal plane and find that, in certain limits, it admi…
An N=1 duality cascade from a deformation of N=4 SUSY Yang-Mills
本文研究了N=1超共形理论的相应形变，它是U（N）N=4超对称Yang-Mills的一个精确的边缘形变.由此产生的理论有一个经典的Higgs分支，它是一个复杂的变形的orbifold C^3/Z_n x Z_n，这是一个非紧的Calabi-Yau空间与孤立的锥状奇点。在模空间中的这些奇点处，理论表现出对偶级联，并流向具有质量间隙的限制理论。通过精确求解相应的全纯矩阵模型，我们计算了对偶级联末端产生的精确量子超势，并精确计算了量子效应如何通过用有限大小的三圈代替锥奇异性来变形经典模空间。局部的结构是变形的锥状，但整体的几何形状是不同的。这种去奇异化的量子形变几何是在对偶级联末端的探测D3-膜的模空间，该对偶级联实现在具有离散挠率的轨道C^3/Z_n x Z_n的形变中的孤立锥状奇点处的（分数）D3-膜的世界体积上。
The moduli space of toroidal type I vacua, which are consistent at the non-perturbative level, consists of independent branches characterized by the number (0, 16 or 32) of rigid branes sitting on top of orientifold planes. This structure persists also when supersymmetry is spontaneously broken a la Scherk-Schwarz. We show that all the components of the moduli space in dimension $D\ge 5$ indeed admit heterotic dual components, by explicitly constructing heterotic-type I dual pairs with the rank of the gauge group reduced by 0, 8 or 16 units. In the presence of spontaneous breaking of supersymm…
We investigate supersymmetry (SUSY) breaking scenarios where both SUSY and Lorentz symmetry are broken spontaneously. For concreteness, we propose models in which scalar fluid or vector condensation breaks Lorentz symmetry and accordingly SUSY. Then, we examine whether such scenarios are viable for realistic model buildings. We find, however, that the scalar fluid model suffers from several issues. Then, we extend it to a vector condensation model, which avoids the issues in the scalar fluid case. We show that accelerated expansion and soft SUSY breaking in matter sector can be achieved. In ou…
In this paper we study the large $N$ limit of four-dimensional Supersymmetric Yang-Mills on the lattice using twisted reduced models. We have generated configurations with dynamical massive gluinos and various lattice 't Hooft couplings, and verified that the Pfaffian remains positive. We have determined the lattice spacing in terms of various observables obtaining compatible results. Extrapolating to the massless gluino limit we obtain the lattice spacing dependence on the bare couplings for the supersymmetric theory. The observed dependence goes along the expected behaviour predicted by pert…
