اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدExactly Marginal Operators and Duality in Four Dimensional N=1 Supersymmetric Gauge Theory
311
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We show that manifolds of fixed points, which are generated by exactly marginal operators, are common in N=1 supersymmetric gauge theory. We present a unified and simple prescription for identifying these operators, using tools similar to those employed in two-dimensional N=2 supersymmetry. In particular we rely on the work of Shifman and Vainshtein relating the $bt$-function of the gauge coupling to the anomalous dimensions of the matter fields. Finite N=1 models, which have marginal operators at zero coupling, are easily identified using our approach. The method can also be employed to find manifolds of fixed points which do not include the free theory; these are seen in certain models with product gauge groups and in many non-renormalizable effective theories. For a number of our models, S-duality may have interesting implications. Using the fact that relevant perturbations often cause one manifold of fixed points to flow to another, we propose a specific mechanism through which the N=1 duality discovered by Seiberg could be associated with the duality of finite N=2 models.
قيم البحث
اقرأ أيضاً
A formulation of (non-anticommutative) N=1/2 supersymmetric U(N) gauge theory in noncommutative space is studied. We show that at one loop UV/IR mixing occurs. A generalization of Seiberg-Witten map to noncommutative and non-anticommutative supersp
ace is employed to obtain an action in terms of commuting fields at first order in the noncommutativity parameter tetha. This leads to abelian and non-abelian gauge theories whose supersymmetry transformations are local and non-local, respectively.
A solution to the infinite coupling problem for N=2 conformal supersymmetric gauge theories in four dimensions is presented. The infinitely-coupled theories are argued to be interacting superconformal field theories (SCFTs) with weakly gauged flavor
groups. Consistency checks of this proposal are found by examining some low-rank examples. As part of these checks, we show how to compute new exact quantities in these SCFTs: the central charges of their flavor current algebras. Also, the isolated rank 1 E_6 and E_7 SCFTs are found as limits of Lagrangian field theories.
We compute the supersymmetric partition function of $mathcal{N}{=}1$ supersymmetric gauge theories with an $R$-symmetry on $mathcal{M}_4 cong mathcal{M}_{g,p}times S^1$, a principal elliptic fiber bundle of degree $p$ over a genus-$g$ Riemann surface
, $Sigma_g$. Equivalently, we compute the generalized supersymmetric index $I_{mathcal{M}_{g,p}}$, with the supersymmetric three-manifold ${mathcal{M}_{g,p}}$ as the spatial slice. The ordinary $mathcal{N}{=}1$ supersymmetric index on the round three-sphere is recovered as a special case. We approach this computation from the point of view of a topological $A$-model for the abelianized gauge fields on the base $Sigma_g$. This $A$-model---or $A$-twisted two-dimensional $mathcal{N}{=}(2,2)$ gauge theory---encodes all the information about the generalized indices, which are viewed as expectations values of some canonically-defined surface defects wrapped on $T^2$ inside $Sigma_g times T^2$. Being defined by compactification on the torus, the $A$-model also enjoys natural modular properties, governed by the four-dimensional t Hooft anomalies. As an application of our results, we provide new tests of Seiberg duality. We also present a new evaluation formula for the three-sphere index as a sum over two-dimensional vacua.
Similarly to the bosonic Liouville theory, the $mathcal{N}=2$ supersymmetric Liouville theory was conjectured to be equipped with the duality that exchanges the superpotential and the Kahler potential. The conjectured duality, however, seems to suffe
r from a mismatch of the preserved symmetries. More than fifteen years ago, when I was a student, my supervisor Tohru Eguchi gave a beautiful resolution of the puzzle when the supersymmetry is enhanced to $mathcal{N}=4$ based on his insight into the underlying geometric structure of the $A_1$ singularity. I will review his unpublished but insightful idea and present our attempts to extend it to more general cases.
We calculate the instanton partition function of the four-dimensional N=2* SU(N) gauge theory in the presence of a generic surface operator, using equivariant localization. By analyzing the constraints that arise from S-duality, we show that the effe
ctive twisted superpotential, which governs the infrared dynamics of the two-dimensional theory on the surface operator, satisfies a modular anomaly equation. Exploiting the localization results, we solve this equation in terms of elliptic and quasi-modular forms which resum all non-perturbative corrections. We also show that our results, derived for monodromy defects in the four-dimensional theory, match the effective twisted superpotential describing the infrared properties of certain two-dimensional sigma models coupled either to pure N=2 or to N=2* gauge theories.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
