Anomaly-corrected supersymmetry algebra and supersymmetric holographic renormalization

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 anomalies. Moreover, we show that these anomalies satisfy the Wess-Zumino consistency condition. The super-Weyl anomaly implies that the fermionic operators of the dual field theory, such as the supercurrent, do not transform as tensors under rigid supersymmetry on backgrounds that admit a conformal Killing spinor, and their anticommutator with the conserved supercharge contains anomalous terms. This property is explicitly checked for a toy model. Finally, using the anomalous transformation of the supercurrent, we obtain the anomaly-corrected supersymmetry algebra on curved backgrounds admitting a conformal Killing spinor.Comment: 51 pages; v2: two references added, typos corrected, a discussion about the 2-dimensional super-Weyl anomaly added in section

On the Divisibility of Trinomials by Maximum Weight Polynomials over F2

Divisibility of trinomials by given polynomials over finite fields has been studied and used to construct orthogonal arrays in recent literature. Dewar et al.\ (Des.\ Codes Cryptogr.\ 45:1-17, 2007) studied the division of trinomials by a given pentanomial over \F_2 to obtain the orthogonal arrays of strength at least 3, and finalized their paper with some open questions. One of these questions is concerned with generalizations to the polynomials with more than five terms. In this paper, we consider the divisibility of trinomials by a given maximum weight polynomial over \F_2 and apply the result to the construction of the orthogonal arrays of strength at least 3.Comment: 10 pages, 1 figur

Various Aspects of Holographic Renormalization

In this thesis we explore various aspects of holographic renormalization. The thesis comprises the work done by the candidate during the doctorate programme at SISSA and ICTP under the supervision of A. Tanzini. This consists in the following works. \begin{itemize} \item In \cite{An:2016fzu}, reproduced in chapter \ref{asy-conical} we consider holographic renormalization in an exotic spacetime such as an asymptotically conical manifold, showing that it has a close relation with variational principle. The variational problem of gravity theories is directly related to black hole thermodynamics. For asymptotically locally AdS backgrounds it is known that holographic renormalization results in a variational principle in terms of equivalence classes of boundary data under the local asymptotic symmetries of the theory, which automatically leads to finite conserved charges satisfying the first law of thermodynamics. We show that this connection holds well beyond asymptotically AdS black holes. In particular, we formulate the variational problem for $\mathcal{N}=2$ STU supergravity in four dimensions with boundary conditions corresponding to those obeyed by the so-called `subtracted geometries'. We show that such boundary conditions can be imposed covariantly in terms of a set of asymptotic second class constraints, and we derive the appropriate boundary terms that render the variational problem well posed in two different duality frames of the STU model. This allows us to define finite conserved charges associated with any asymptotic Killing vector and to demonstrate that these charges satisfy the Smarr formula and the first law of thermodynamics. Moreover, by uplifting the theory to five dimensions and then reducing on a 2-sphere, we provide a precise map between the thermodynamic observables of the subtracted geometries and those of the BTZ black hole. Surface terms play a crucial role in this identification. \item In \cite{An:2017ihs}, reproduced in chapter \ref{susy-holo} 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 anomalies. Moreover, we show that these anomalies satisfy the Wess-Zumino consistency condition. The super-Weyl anomaly implies that the fermionic operators of the dual field theory, such as the supercurrent, do not transform as tensors under rigid supersymmetry on backgrounds that admit a conformal Killing spinor, and their anticommutator with the conserved supercharge contains anomalous terms. This property is explicitly checked for a toy model. Finally, using the anomalous transformation of the supercurrent, we obtain the anomaly-corrected supersymmetry algebra on curved backgrounds admitting a conformal Killing spinor. \end{itemize

Black hole thermodynamics from a variational principle: asymptotically conical backgrounds

The variational problem of gravity theories is directly related to black hole thermodynamics. For asymptotically locally AdS backgrounds it is known that holographic renormalization results in a variational principle in terms of equivalence classes of boundary data under the local asymptotic symmetries of the theory, which automatically leads to finite conserved charges satisfying the first law of thermodynamics. We show that this connection holds well beyond asymptotically AdS black holes. In particular, we formulate the variational problem for $\mathcal{N}=2$ STU supergravity in four dimensions with boundary conditions corresponding to those obeyed by the so called `subtracted geometries'. We show that such boundary conditions can be imposed covariantly in terms of a set of asymptotic second class constraints, and we derive the appropriate boundary terms that render the variational problem well posed in two different duality frames of the STU model. This allows us to define finite conserved charges associated with any asymptotic Killing vector and to demonstrate that these charges satisfy the Smarr formula and the first law of thermodynamics. Moreover, by uplifting the theory to five dimensions and then reducing on a 2-sphere, we provide a precise map between the thermodynamic observables of the subtracted geometries and those of the BTZ black hole. Surface terms play a crucial role in this identification

The Effects of Air Pollution on Mortality in South Korea

AbstractIt is well known that air pollution has the negative effect on human health. This study is dealt with the relationship between air pollutant level and standardized mortality between 2005 and 2013 in Korea. The standardized mortality are collected by the 251 administrative districts using KOSIS (Korean Statistical Information Service) and the air pollutant data collected from air pollutant monitoring sites. The statistical interpolation technique is adapted to solve the problem of spatial misalignment between air pollutant and administrative districts. In addition, SaTScan is used to detecting the high relatively risk area based on spatial and temporal characteristics. It can help determining other external factors to mortality

Successive spin-flop transitions of a Neel-type antiferromagnet Li2MnO3 single crystal with a honeycomb lattice

We have carried out high magnetic field studies of single-crystalline Li2MnO3, a honeycomb lattice antiferromagnet. Its magnetic phase diagram was mapped out using magnetization measurements at applied fields up to 35 T. Our results show that it undergoes two successive meta-magnetic transitions around 9 T fields applied perpendicular to the ab plane (along the c* axis). These phase transitions are completely absent in the magnetization measured with the field applied along the ab plane. In order to understand this magnetic phase diagram, we developed a mean-field model starting from the correct Neel-type magnetic structure, consistent with our single crystal neutron diffraction data at zero field. Our model calculations succeeded in explaining the two meta-magnetic transitions that arise when Li2MnO3 enters two different spin-flop phases from the zero field Neel phase.open1187Nsciescopu