Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userHarmonicity in N=4 supersymmetry and its quantum anomaly
156
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The holomorphicity property of N=1 superpotentials or of N=2 F-terms involving vector multiplets is generalized to the case of N=4 1/2-BPS effective operators defined in harmonic superspace. The resulting harmonicity equations are shown to control the moduli dependence of the couplings of higher dimensional operators involving powers of the N=4 Weyl superfield, computed by N=4 topological amplitudes. These equations can also be derived on the string side, exhibiting an anomaly from world-sheet boundary contributions that leads to recursion relations for the non-analytic part of the couplings.
rate research
Read More
In the context of the superconformal N=4 SYM theory the Konishi anomaly can be viewed as the descendant $K_{10}$ of the Konishi multiplet in the 10 of SU(4), carrying the anomalous dimension of the multiplet. Another descendant $O_{10}$ with the same quantum numbers, but this time without anomalous dimension, is obtained from the protected half-BPS operator $O_{20}$ (the stress-tensor multiplet). Both $K_{10}$ and $O_{10}$ are renormalized mixtures of the same two bare operators, one trilinear (coming from the superpotential), the other bilinear (the so-called quantum Konishi anomaly). Only the operator $K_{10}$ is allowed to appear in the right-hand side of the Konishi anomaly equation, the protected one $O_{10}$ does not match the conformal properties of the left-hand side. Thus, in a superconformal renormalization scheme the separation into classical and quantum anomaly terms is not possible, and the question whether the Konishi anomaly is one-loop exact is out of context. The same treatment applies to the operators of the BMN family, for which no analogy with the traditional axial anomaly exists. We illustrate our abstract analysis of this mixing problem by an explicit calculation of the mixing matrix at level g^4 (two loops) in the supersymmetric dimensional reduction scheme.
We show that CP-violating Weyl anomaly induces a supersymmetry anomaly in the formulation of superconformal supergravity as is observed in CP-preserving cases. This supersymmetry anomaly can be removed in the old minimal supergravity by adding suitable local counterterms, and it becomes a consistent theory.
The supersymmetry transformation relating the Konishi operator to its lowest descendant in the 10 of SU(4) is not manifest in the N=1 formulation of the theory but rather uses an equation of motion. On the classical level one finds one operator, the unintegrated chiral superpotential. In the quantum theory this term receives an admixture by a second operator, the Yang-Mills part of the Lagrangian. It has long been debated whether this anomalous contribution is affected by higher loop corrections. We present a first principles calculation at the second non-trivial order in perturbation theory using supersymmetric dimensional reduction as a regulator and renormalisation by Z-factors. Singular higher loop corrections to the renormalisation factor of the Yang-Mills term are required if the conformal properties of two-point functions are to be met. These singularities take the form determined in preceding work on rather general grounds. Moreover, we also find non-vanishing finite terms. The core part of the problem is the evaluation of a four-loop two-point correlator which is accomplished by the Laporta algorithm. Apart from several examples of the T1 topology with two lines of non-integer dimension we need the first few orders in the epsilon expansion of three master integrals. The approach is self-contained in that all the necessary information can be derived from the power counting finiteness of some integrals.
We present the class of deformations of simple Euclidean superalgebra, which describe the supersymmetrization of some Lie algebraic noncommutativity of D=4 Euclidean space-time. The presented deformations are generated by the supertwists. We provide new explicit formulae for a chosen twisted D=4 Euclidean Hopf superalgebra and describe the corresponding quantum covariant deformation of chiral Euclidean superspace.
N=4 Poincare supergravity has a global SU(1,1) duality symmetry that acts manifestly only on shell as it involves duality rotations of vector fields. A U(1) subgroup of this symmetry is known to be anomalous at the quantum level in the presence of a non-trivial gravitational background. We first derive this anomaly from a novel perspective, by relating it to a similar anomaly in conformal supergravity where SU(1,1) acts off shell, using the fact that N=4 Poincare supergravity has a superconformal formulation. We explicitly construct the corresponding local and nonlocal anomalous terms in the one-loop effective action. We then study how this anomaly is reflected in the supergravity S-matrix. Calculating one-loop N=4 supergravity scattering amplitudes (with and without additional matter multiplets) using color/kinematics duality and the double-copy construction we find that a particular U(1) symmetry which was present in the tree-level amplitudes is broken at the quantum level. This breaking manifests itself in the appearance of new one-loop N=4 supergravity amplitudes that have non-vanishing soft-scalar limits (these amplitudes are absent in N>4 supergravities). We discuss the relation between these symmetry-violating amplitudes and the corresponding U(1) anomalous term in the one-loop supergravity effective action.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
