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.
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.
We consider the $U(1) ^{n}$ extension of the effective $\mathcal{N}=2$ supersymmetric $U(1) \times U(1) $ model of $arXiv:1204.2141$; and study the explicit relationship between partial breaking of $\mathcal{N}=2$ supersymmetry constraint and D3 brane tadpole anomaly of type IIB string on Calabi-Yau threefolds in presence of H$^{RR}$ and H$^{NS}$ fluxes. We also comment on supersymmetry breaking in the particular $\mathcal{N}=2$ $U(1) $ Maxwell theory; and study its interpretation in connection with the tadpole anomaly with extra localized flux sources.
We showed that there is no SU(2) Witten anomaly in a large class of 4d N = 2 supersymmetric Heterotic string compactifications. The consistency conditions we consider are the modularity of the new supersymmetric index, the integrality of BPS indices, and the discrete Peccei-Quinn shift symmetries. We also found an example where these conditions are not sufficient to show that the theory is anomaly free. This suggests that there are more conditions in the worldsheet SCFT essential for consistent string compactifications.
Operators transform anomalously under the symmetry in the presence of quantum anomalies. We study this aspect of the super-Weyl anomaly in $\mathcal N=(1,1)$ superconformal field theories (SCFTs), in the context of AdS/CFT. In particular, we carry out holographic renormalization for $(1,1)$ pure AdS$_3$ supergravity that is supposed to be a gravity dual of the $\mathcal N=(1,1)$ SCFT, and derive holographic superconformal Ward identities with corresponding anomalies. We show that the obtained super-Weyl anomaly of the $\mathcal N=(1,1)$ SCFT induces a quantum correction term in the transformat…
We present a comprehensive analysis of supersymmetry anomalies in the free and massless Wess-Zumino (WZ) model in perturbation theory. At the classical level the model possesses ${\mathcal N}=1$ superconformal symmetry, which is partially broken by quantum anomalies. The form of the anomalies and the part of the symmetry they break depend on the multiplet of conserved currents used. It was previously shown that the R-symmetry anomaly of the conformal current multiplet induces an anomaly in Q-supersymmetry, which appears first in 4-point functions. Here we confirm this result by an explicit 1-l…
We present a BRST analysis of supersymmetry anomalies of $\mathcal{N} = 1$ supersymmetric quantum field theories with anomalous R symmetry. To this end, we consider the coupling of the matter theory to classical $\mathcal{N} = 1$ new minimal supergravity. We point out that a supersymmetry anomaly cocycle associated to the $\mathrm{U}(1){}_\mathrm{R}$ field does exist for this theory. It is non-trivial in the space of supergravity fields (and ghosts), but it becomes BRST-exact in the functional space that includes antifields. Equivalently, the $\mathrm{U}(1){}_\mathrm{R}$ supersymmetry anomaly …
We determine the general structure of quantum anomalies for the $R$-multiplet of four dimensional $\mathcal{N}=1$ supersymmetric quantum field theories in the presence of background fields for an arbitrary number of Abelian flavor multiplets. By solving the Wess-Zumino consistency conditions for off-shell new minimal supergravity in four dimensions with an arbitrary number of Abelian vector multiplets, we compute the anomaly in the conservation of the supercurrent to leading non trivial order in the gravitino and vector multiplet fermions. We find that both $R$-symmetry and flavor anomalies ne…
We consider recent claims that supersymmetry is anomalous in the presence of a R-symmetry anomaly. We revisit arguments that such an anomaly in supersymmetry can be removed and write down an explicit counterterm that accomplishes it. Removal of the supersymmetry anomaly requires enlarging the corresponding current multiplet. As a consequence the Ward identities for other symmetries that are already anomalous acquire extra terms. This procedure can only be impeded when the choice of current multiplet is forced. We show how Wess-Zumino consistency conditions are modified when the anomaly is remo…
We revisit quantum field theory anomalies, emphasizing the interplay with diffeomorphisms and supersymmetry. The Ward identities of the latter induce Noether currents of all continuous symmetries, and we point out how these consistent currents are replaced by their covariant form through the appearance of the Bardeen-Zumino currents, which play a central role in our study. For supersymmetry Ward identities, two systematic methods for solving the Wess-Zumino consistency conditions are discussed: anomaly inflow and anomaly descent. The simplest inflows are from supersymmetric Chern-Simons action…
We show that supersymmetry is anomalous in ${\cal N}=1$ superconformal quantum field theories (SCFTs) with an anomalous R-symmetry. This anomaly was originally found in holographic SCFTs at strong coupling. Here we show that this anomaly is present in general and demonstrate it for the massless superconformal Wess-Zumino model via a one loop computation. The anomaly appears first in four-point functions of two supercurrents with either two R-currents or with an R-current and an energy momentum tensor. In fact, the Wess-Zumino consistency conditions together with the standard R-symmetry anomaly…
A canonical quantization scheme applied to a classical supersymmetric system with quadratic in momentum supercharges gives rise to a quantum anomaly problem described by a specific term to be quadratic in Planck constant. We reveal a close relationship between the anomaly and the Schwarzian derivative, and specify a quantization prescription which generates the anomaly-free supersymmetric quantum system with second order supercharges. We also discuss the phenomenon of a coupling-constant metarmorphosis that associates quantum systems with first-order supersymmetry to the systems with the secon…
Positivity Constraints on Anomalies and Supersymmetry
四维超对称理论中迹线与R流反常之间的关系表明，在N=1 Seiberg对偶性研究中匹配的U（1）$_R$ F $^2$，U（1）$_R$和U（1）$^3_R$反常满足正性约束.这些约束在大量的N=1的超对称规范理论中的非阿贝尔库仑相位进行了测试，它们满足所有的重整化模型与唯一的反常自由的R-电流，包括那些偶然对称。最引人注目的事实是，流动的欧拉异常系数，$a_{UV}-a_{IR}$，始终是积极的，作为所阐明的卡迪。
We present a systematic approach to supersymmetric holographic renormalization for a generic 5D $\mathcal{N}=2$ gauged supergravity theory with matter multiplets, including its fermionic sector, with all gauge fields consistently set to zero. We determine the complete set of supersymmetric local boundary counterterms, including the finite counterterms that parameterize the choice of supersymmetric renormalization scheme. This allows us to derive holographically the superconformal Ward identities of a 4D superconformal field theory on a generic background, including the Weyl and super-Weyl anom…
We find a class of scale-anomaly-free $\mathcal{N}=2$ supersymmetric quantum systems with non-vanishing potential terms where space and time scale with distinct exponents. Our results generalise the known case of the supersymmetric inverse square potential to a larger class of scaling symmetries.
