Ultraviolet behaviour of higher spin gauge field propagators and one loop mass renormalization

The ultraviolet singular structure of the bulk-to-bulk propagators for higher spin gauge fields in AdS₄${\mathit{AdS}}_4$ space is analyzed in details. Possible interactions with the Higgs scalar and the corresponding one loop mass renormalization are studied. This mass renormalization is finite and connected with the anomalous dimensions of those currents in the corresponding boundary CFT₃${\mathit{CFT}}_3$ that cease to be conserved when the interaction is switched on. In particular it is proportional to ?−2$?-2$.     

On the anatomy of multi-spin magnon and single spike string solutions

We study rigid string solutions rotating in AdS₅×S⁵${\mathit{AdS}}_5\times S^5$ background. For particular values of the parameters of the solutions we find multispin solutions corresponding to giant magnons and single spike strings. We present an analysis of the dispersion relations in the case of three spin solutions distributed only in S⁵$S^5$ and the case of one spin in AdS₅${\mathit{AdS}}_5$ and two spins in S⁵$S^5$. The possible relation of these string solutions to gauge theory operators and spin chains are briefly discussed.     

Dynamical SUSY breaking in heterotic M-theory

It is shown that four-dimensional N=1$N=1$ supersymmetric QCD with massive flavors in the fundamental representation of the gauge group can be realized in the hidden sector of E₈×E₈$E_8\times E_8$ heterotic string vacua. The number of flavors can be chosen to lie in the range of validity of the free-magnetic dual, using which one can demonstrate the existence of long-lived meta-stable non-supersymmetric vacua. This is shown explicitly for the gauge group Spin(10)$\mathit{Spin}(10)$, but the methods are applicable to Spin(Nc)$\mathit{Spin}(N_c)$, SU(Nc)$\mathit{SU}(N_c)$ and Sp(Nc)$\mathit{Sp}(N_c)$ for a wide range of color index Nc$N_c$. Hidden sectors of this type can potentially be used as a mechanism to break supersymmetry within the context of heterotic M-theory.     

Non-Abelian fusion rules from an Abelian system

We demonstrate the emergence of non-Abelian fusion rules for excitations of a two dimensional lattice model built out of Abelian degrees of freedom. It can be considered as an extension of the usual toric code model on a two dimensional lattice augmented with matter fields. It consists of the usual C(Z_p)$\mathbb{C}\left({\mathbb{Z}}_p\right)$ gauge degrees of freedom living on the links together with matter degrees of freedom living on the vertices. The matter part is described by a n$n$ dimensional vector space which we call H_n$H_n$. The Z_p${\mathbb{Z}}_p$ gauge particles act on the vertex particles and thus H_n$H_n$ can be thought of as a C(Z_p)$\mathbb{C}\left({\mathbb{Z}}_p\right)$ module. An exactly solvable model is built with operators acting in this Hilbert space. The vertex excitations for this model are studied and shown to obey non-Abelian fusion rules. We will show this for specific values of n$n$ and p$p$, though we believe this feature holds for all n>p$n>p$. We will see that non-Abelian anyons of the quantum double of C(S₃)$\mathbb{C}\left(S_3\right)$ are obtained as part of the vertex excitations of the model with n=6$n=6$ and p=3$p=3$. Ising anyons are obtained in the model with n=4$n=4$ and p=2$p=2$. The n=3$n=3$ and p=2$p=2$ case is also worked out as this is the simplest model exhibiting non-Abelian fusion rules. Another common feature shared by these models is that the ground states have a higher symmetry than Z_p${\mathbb{Z}}_p$. This makes them possible candidates for realizing quantum computation.     

Superconformal invariants or how to relate four-point AdS amplitudes

Using the form of N=2$N=2$ superconformal invariants we derive the explicit relation between the bottom and top components of the correlator of four stress-tensor multiplets in N=4$N=4$ super-Yang–Mills. The result is given in terms of an eighth order differential operator acting on the function of two variables which characterises these correlators. It allows us to show a non-trivial consistency relation between the known results for the corresponding supergravity amplitudes on AdS₅${\mathit{AdS}}_5$.     

Exact expressions for quantum corrections to spinning strings

The one-loop worldsheet quantum corrections to the energy of spinning strings on R×S³$\mathbb{R}\times S^3$ within AdS₅×S⁵${\mathit{AdS}}_5\times S^5$ are reexamined. The explicit expansion in the effective 't Hooft coupling λ^′=λ/J²${\lambda }^{\prime }=\lambda /J^2$ is rigorously derived. The expansion contains both analytic and non-analytic terms in λ^′${\lambda }^{\prime }$, as well as exponential corrections. Furthermore, we pin down the origin of the terms that are not captured by the quantum string Bethe ansatz, which only produces analytic terms in λ^′${\lambda }^{\prime }$. It is shown that the analytic terms arise from string fluctuations within the S³$S^3$, whereas the non-analytic and exponential terms, which are not captured by the Bethe ansatz, originate from the fluctuations in all directions within the supersymmetric sigma model on AdS₅×S⁵${\mathit{AdS}}_5\times S^5$. We also comment on the case of spinning string in AdS₃×S¹${\mathit{AdS}}_3\times S^1$.     

Some properties of the Alday–Maldacena minimum

The Alday–Maldacena solution, relevant to the n=4$n=4$ gluon amplitude in N=4$N=4$ SYM at strong coupling, was recently identified as a minimum of the regularized action in the moduli space of solutions of the AdS₅${\mathit{AdS}}_5$σ  -model equations of motion. Analogous solutions of the Nambu–Goto equations for the n=4$n=4$ case are presented and shown to form (modulo the reparametrization group) an equally large but different moduli space, with the Alday–Maldacena solution at the intersection of the σ  -model and Nambu–Goto moduli spaces. We comment upon the possible form of the regularized action for n=5$n=5$. A function of moduli parameters za$z_a$ is written, whose minimum reproduces the BDDK one-loop five-gluon amplitude. This function may thus be considered as some kind of Legendre transform of the BDDK formula and has its own value independently of the Alday–Maldacena approach.     

O-BTZ: Orientifolded BTZ black hole

Banados–Teitelboim–Zanelli (BTZ) black holes are constructed by orbifolding AdS₃ geometry by boost transformations of its O(2,2)$O(2,2)$ isometry group. Here we construct a new class of solutions to AdS₃ Einstein gravity, orientifolded BTZ or O-BTZ   for short, which in general, besides the usual BTZ orbifolding, involve orbifolding (orientifolding) by a Z₂${\mathbb{Z}}_2$ part of O(2,2)$O(2,2)$ isometry group. This Z₂${\mathbb{Z}}_2$ is chosen such that it changes the orientation on AdS₃ while keeping the orientation on its 2D conformal boundary. O-BTZ solutions exhaust all un-oriented AdS₃ black hole solutions, as BTZ black holes constitute all oriented AdS₃ black holes. O-BTZ, similarly to BTZ black holes, are stationary, axisymmetric asymptotically AdS₃ geometries with two asymptotic charges, mass and angular momentum.     

Properties of CFTs dual to charged BTZ black hole

We study properties of strongly coupled CFT's with non-zero background electric charge in 1+1$1+1$ dimensions by studying the dual gravity theory—which is a charged BTZ black hole. Correlators of operators dual to scalars, gauge fields and fermions are studied at both T=0$T=0$ and T≠0$T\ne 0$. In the T=0$T=0$ case we are also able to compare with analytical results based on AdS₂${\mathit{AdS}}_2$ and find reasonable agreement. In particular the correlation between log periodicity and the presence of finite spectral density of gapless modes is seen. The real part of the conductivity (given by the current–current correlator) also vanishes as ω→0$\omega \to 0$ as expected. The fermion Green's function shows quasiparticle peaks with approximately linear dispersion but the detailed structure is neither Fermi liquid nor Luttinger liquid and bears some similarity to a “Fermi–Luttinger” liquid. This is expected since there is a background charge and the theory is not Lorentz or scale invariant. A boundary action that produces the observed non-Luttinger liquid like behavior (k  -independent non-analyticity at ω=0$\omega =0$) in the Green's function is discussed.     

Magnon-like dispersion relation from M-theory

We investigate classical rotating membranes in two different backgrounds. First, we obtain membrane solution in AdS₄×S⁷${\mathit{AdS}}_4\times S^7$ background, analogous to the solution obtained by Hofman and Maldacena in the case of string theory. We find a magnon type dispersion relation similar to that of Hofman and Maldacena and to the one found by Dorey for the two spin case. In the appendix of the paper, we consider membrane solutions in AdS₇×S⁴${\mathit{AdS}}_7\times S^4$, which give new relations between the conserved charges.     

Weak mirror symmetry of complex symplectic Lie algebras

A complex symplectic structure on a Lie algebra h$\mathfrak{h}$ is an integrable complex structure J$J$ with a closed non-degenerate (2,0)$(2,0)$-form. It is determined by J$J$ and the real part Ω$\Omega$ of the (2,0)$(2,0)$-form. Suppose that h$\mathfrak{h}$ is a semi-direct product g?V$\mathfrak{g}?V$, and both g$\mathfrak{g}$ and V$V$ are Lagrangian with respect to Ω$\Omega$ and totally real with respect to J$J$. This note shows that g?V$\mathfrak{g}?V$ is its own weak mirror image in the sense that the associated differential Gerstenhaber algebras controlling the extended deformations of Ω$\Omega$ and J$J$ are isomorphic.     

Confined hidden vector dark matter

We argue that the lightest vector bound states of a confining hidden sector communicating with the Standard Model through the Higgs portal are stable and are viable candidates of dark matter. The model is based on an SU(2)$\mathit{SU}(2)$ gauge group with a scalar field in its fundamental representation and the stability of the lightest vector bound state results from the existence of a custodial symmetry. As the relic density depends essentially on the scale of confinement in the hidden sector, ΛHS${\Lambda }_{\mathrm{HS}}$, agreement with WMAP abundance requires ΛHS${\Lambda }_{\mathrm{HS}}$ in the 20–120 TeV range.     

Fluxmetric and magnetometric demagnetizing factors for cylinders

Fluxmetric and magnetometric demagnetizing factors, _Nf$N_{\mathrm{f}}$ and _Nm$N_{\mathrm{m}}$, for cylinders along the axial direction are numerically calculated as functions of material susceptibility χ$\chi$ and the ratio γ$\gamma$ of length to diameter. The results have an accuracy better than 0.1% with respect to min(_Nf,m,1-_Nf,m)$\min (N_{\mathrm{f},\mathrm{m}},1-N_{\mathrm{f},\mathrm{m}})$ and are tabulated in the range of 0.01?γ?500$0.01?\gamma ?500$ and -1?χ<∞$-1?\chi <\infty$. _Nm$N_{\mathrm{m}}$ along the radial direction is evaluated with a lower accuracy from _Nm$N_{\mathrm{m}}$ along the axis and tabulated in the range of 0.01?γ?1$0.01?\gamma ?1$ and -1?χ<∞$-1?\chi <\infty$. Some previous results are discussed and several applications are explained based on the new results.     

New massive gravity domain walls

The properties of the asymptotic AdS₃${\mathit{AdS}}_3$ space–times representing flat domain walls (DW's) solutions of the new massive 3D gravity with scalar matter are studied. Our analysis is based on first order BPS-like equations involving an appropriate superpotential. The Brown–York boundary stress-tensor is used for the calculation of DW's tensions as well as of the CFT₂${\mathit{CFT}}_2$ central charges. The holographic renormalization group flows and the phase transitions in specific deformed CFT₂${\mathit{CFT}}_2$ dual to 3D massive gravity model with quadratic superpotential are discussed.