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.     

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${\mathit{AdS}}_3\times S^1$.     

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.     

Ricci-flat and charged wormholes in five dimensions

We construct stationary Ricci-flat inter-universe Lorentzian wormhole solutions in all D?5$D?5$ dimensions that connect two flat asymptotic spacetimes. Such a solution can be viewed as the gravity dual of a string tachyon state whose linear momentum is larger than its tension. We focus our analysis on the D=5$D=5$ wormholes which are not traversable for the timelike and null geodesics; however, we demonstrate that there exist accelerated timelike trajectories that traverse from one asymptotic region to the other. We further study the minimally-coupled scalar wave equation and demonstrate that the quantum tunnelling between two worlds must occur. We also obtain charged wormholes in five-dimensional supergravities. With appropriate choice of parameters, these wormholes connect AdS₃×S²${\mathit{AdS}}_3\times S^2$ in one asymptotic region to flat Minkowskian spacetime in the other.     

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$?-2$.     

Mesons and Higgs branch in defect theories

We consider the defect theory obtained by intersecting D3- and D5-branes along two common spatial directions. We work in the approximation in which the D5-brane is a probe in the AdS₅×S⁵${\mathit{AdS}}_5\times S^5$ background. By adding worldvolume flux to the D5-brane and choosing an appropriate embedding of the probe in AdS₅×S⁵${\mathit{AdS}}_5\times S^5$, one gets a supersymmetric configuration in which some of the D3-branes recombine with the D5-brane. We check this fact by showing that the D5-brane can be regarded as a system of polarized D3-branes. On the field theory side this corresponds to the Higgs branch of the defect theory, where some of the fundamental hypermultiplet fields living on the intersection acquire a vacuum expectation value. We study the spectrum of mesonic bound states of the defect theory in this Higgs branch and show that it is continuous and gapless.     

Two-dimensional gauge theory and matrix model

We study a matrix model obtained by dimensionally reducing Chern–Simons theory on S³$S^3$. We find that the matrix integration is decomposed into sectors classified by the representation of SU(2)$\mathit{SU}(2)$. We show that the N  -block sectors reproduce SU(N)$\mathit{SU}(N)$ Yang–Mills theory on S²$S^2$ as the matrix size goes to infinity.     

Galilean anti-de-Sitter spacetime in Romans theory

The Romans type IIA theory is the only known example of 10-dimensional maximal supergravity where (tensor) fields are explicitly massive. We provide an example of a non-relativistic anti-de-Sitter NRadS₄×S⁶${\mathit{NRadS}}_4\times S^6$ background as a solution in massive type IIA. A compactification of which on S⁶$S^6$ gives immediately the prototype NRadS background in D=4$D=4$ which is proposed to be dual to ‘cold atoms’ or unitary fermions on a wire.     

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.     

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.     

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${\mathit{AdS}}_5$.     

Bertrand curves in the three-dimensional sphere

A curve α$\alpha$ immersed in the three-dimensional sphere S³${\mathbb{S}}^3$ is said to be a Bertrand curve if there exists another curve β$\beta$ and a one-to-one correspondence between α$\alpha$ and β$\beta$ such that both curves have common principal normal geodesics at corresponding points. The curves α$\alpha$ and β$\beta$ are said to be a pair of Bertrand curves in S³${\mathbb{S}}^3$. One of our main results is a sort of theorem for Bertrand curves in S³${\mathbb{S}}^3$ which formally agrees with the classical one: “Bertrand curves in S³${\mathbb{S}}^3$ correspond to curves for which there exist two constants λ≠0$\lambda \ne 0$ and μ$\mu$ such that λκ+μτ=1$\lambda \kappa +\mu \tau =1$”, where κ$\kappa$ and τ$\tau$ stand for the curvature and torsion of the curve; in particular, general helices in the 3-sphere introduced by M. Barros are Bertrand curves. As an easy application of the main theorem, we characterize helices in S³${\mathbb{S}}^3$ as the only twisted curves in S³${\mathbb{S}}^3$ having infinite Bertrand conjugate curves. We also find several relationships between Bertrand curves in S³${\mathbb{S}}^3$ and (1,3)-Bertrand curves in R⁴${\mathbb{R}}^4$.