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Register a new userSymmetries of curved superspace in five dimensions
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Gabriele Tartaglino-Mazzucchelli
Publication date
2014
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English
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We develop a formalism to construct supersymmetric backgrounds within the superspace formulation for five-dimensional (5D) conformal supergravity given in arXiv:0802.3953. Our approach is applicable to any off-shell formulation for 5D minimal Poincare and anti-de Sitter supergravity theories realized as the Weyl multiplet coupled with two compensators. For those superspace backgrounds which obey the equations of motion for (gauged) supergravity, we naturally reproduce the supersymmetric solutions constructed a decade ago by Gauntlett et al. For certain supersymmetric backgrounds with eight supercharges, we construct a large family of off-shell supersymmetric sigma models such that the superfield Lagrangian is given in terms of the Kahler potential of a real analytic Kahler manifold.
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All five-dimensional non-abelian gauge theories have a $U(1)_I$ global symmetry associated with instantonic particles. We describe an obstruction to coupling $U(1)_I$ to a classical background gauge field that occurs whenever the theory has a one-form center symmetry. This is a finite-order mixed t Hooft anomaly between the two symmetries. We also show that a similar obstruction takes place in gauge theories with fundamental matter by studying twisted bundles for the ordinary flavor symmetry. We explore some general dynamical properties of the candidate phases implied by the anomaly. Finally, we apply our results to supersymmetric gauge theories in five dimensions and analyze the symmetry enhancement patterns occurring at their conjectured RG fixed points.
We study $(2,2)$ and $(4,4)$ supersymmetric theories with superspace higher derivatives in two dimensions. A characteristic feature of these models is that they have several different vacua, some of which break supersymmetry. Depending on the vacuum, the equations of motion describe different propagating degrees of freedom. Various examples are presented which illustrate their generic properties. As a by-product we see that these new vacua give a dynamical way of generating non-linear realizations. In particular, our 2D $(4,4)$ example is the dimensional reduction of a 4D $N=2$ model, and gives a new way for the spontaneous breaking of extended supersymmetry.
Using the superspace formulation for the 5D N = 1 Weyl supermultiplet developed in arXiv:0802.3953, we elaborate the concept of conformally flat superspace in five dimensions. For a large family of supersymmetric theories (including sigma-models and Yang-Mills theories) in the conformally flat superspace, we describe an explicit procedure to formulate their dynamics in terms of rigid 4D N = 1 superfields. The case of 5D N = 1 anti-de Sitter superspace is discussed as an example.
In a {cal N}=1 superspace setup and using dimensional regularization, we give a general and simple prescription to compute anomalous dimensions of composite operators in {cal N}=4, SU(N) supersymmetric Yang-Mills theory, perturbatively in the coupling constant g. We show in general that anomalous dimensions are responsible for the appearance of higher order poles in the perturbative expansion of the two-point function and that their lowest contribution can be read directly from the coefficient of the 1/epsilon^2 pole. As a check of our procedure we rederive the anomalous dimension of the Konishi superfield at order g^2. We then apply this procedure to the case of the double trace, dimension 4, superfield in the 20 of SU(4) recently considered in the literature. We find that its anomalous dimension vanishes for all N in agreement with previous results.
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