Supersymmetric Bethe ansatz and Baxter equations from discrete Hirota dynamics

We show that eigenvalues of the family of Baxter Q  -operators for supersymmetric integrable spin chains constructed with the gl(K|M)$gl(K|M)$-invariant R-matrix obey the Hirota bilinear difference equation. The nested Bethe ansatz for super-spin chains, with any choice of simple root system, is then treated as a discrete dynamical system for zeros of polynomial solutions to the Hirota equation. Our basic tool is a chain of Bäcklund transformations for the Hirota equation connecting quantum transfer matrices. This approach also provides a systematic way to derive the complete set of generalized Baxter equations for super-spin chains.     

Yang–Mills instantons and dyons on group manifolds

We consider Euclidean SU(N)$\mathrm{SU}(N)$ Yang–Mills theory on the space G×R$G\times \mathbb{R}$, where G is a compact semisimple Lie group, and introduce first-order BPS-type equations which imply the full Yang–Mills equations. For gauge fields invariant under the adjoint G  -action these BPS equations reduce to first-order matrix equations, to which we give instanton solutions. In the case of G=SU(2)≅S³$G=\mathrm{SU}(2)\cong S^3$, our matrix equations are recast as Nahm equations, and a further algebraic reduction to the Toda chain equations is presented and solved for the SU(3) example. Finally, we change the metric on G×R$G\times \mathbb{R}$ to Minkowski and construct finite-energy dyon-type Yang–Mills solutions. The special case of G=SU(2)×SU(2)$G=\mathrm{SU}(2)\times \mathrm{SU}(2)$ may be used in heterotic flux compactifications.     

New exact solution structures and nonlinear dispersion in the coupled nonlinear wave systems

In this Letter, to further understand the role of nonlinear dispersion in coupled nonlinear wave systems in both real and complex fields, we study the coupled Klein–Gordon equations with nonlinear dispersion in real field (called CKG(m,n,k)$\mathrm{CKG}(m,n,k)$ equation) and (2+1)$(2+1)$-dimensional generalization of coupled nonlinear Schrödinger equation with nonlinear dispersion in complex field (called GCNLS(m,n,k)$\mathrm{GCNLS}(m,n,k)$ equation) via some transformations. As a consequence, some types of solutions are obtained, which contain compactons, solitary pattern solutions, envelope compacton solutions, envelope solitary pattern solutions, solitary wave solutions and rational solutions.     

The exact decomposition of gauge variables in lattice Yang–Mills theory

In this Letter, we consider lattice versions of the decomposition of the Yang–Mills field a la Cho–Faddeev–Niemi, which was extended by Kondo, Shinohara and Murakami in the continuum formulation. For the SU(N)$\mathit{SU}(N)$ gauge group, we propose a set of defining equations for specifying the decomposition of the gauge link variable and solve them exactly without using the ansatz adopted in the previous studies for SU(2)$\mathit{SU}(2)$ and SU(3)$\mathit{SU}(3)$. As a result, we obtain the general form of the decomposition for SU(N)$\mathit{SU}(N)$ gauge link variables and confirm the previous results obtained for SU(2)$\mathit{SU}(2)$ and SU(3)$\mathit{SU}(3)$.     

Analytic solution of the multiloop Baxter equation

The asymptotic spectrum of anomalous dimensions of gauge-invariant operators in maximally supersymmetric Yang–Mills theory is believed to be described by a long-range integrable spin chain model. We focus in this study on its sl(2)$sl(2)$ subsector spanned by the twist-two single-trace Wilson operators, which are shared by all gauge theories, supersymmetric or not. We develop a formalism for the solution of the perturbative multiloop Baxter equation encoding their asymptotic anomalous dimensions, using Wilson polynomials as basis functions and Mellin transform technique. These considerations yield compact results which allow analytical calculations of multiloop anomalous dimensions bypassing the use of the principle of maximal transcendentality. As an application of our method we analytically confirm the known four-loop result. We also determine the dressing part of the five-loop anomalous dimensions.     

Generalized Knizhnik–Zamolodchikov equations,off-shell Bethe ansatz and non-skew-symmetric classical r-matrices

Using non-skew-symmetric sl(2)$\mathit{sl}(2)$-valued classical r-matrices with spectral parameters we construct a generalization of the Knizhnik–Zamolodchikov (KZ) equations. We obtain integral solutions of the constructed KZ-type equations using the “off-shell” Bethe ansatz technique. We consider several examples of the obtained generalized KZ equations and their integral solutions that correspond to the “K-twisted” non-skew-symmetric classical r-matrices parametrized by arbitrary complex parameter ξ.     

A BRST gauge-fixing procedure for Yang–Mills theory on sphere

A gauge-fixing procedure for the Yang–Mills theory on an n  -dimensional sphere (or a hypersphere) is discussed in a systematic manner. We claim that Adler's gauge-fixing condition used in massless Euclidean QED on a hypersphere is not conventional because of the presence of an extra free index, and hence is unfavorable for the gauge-fixing procedure based on the BRST invariance principle (or simply BRST gauge-fixing procedure). Choosing a suitable gauge condition, which is proved to be equivalent to a generalization of Adler's condition, we apply the BRST gauge-fixing procedure to the Yang–Mills theory on a hypersphere to obtain consistent results. Field equations for the Yang–Mills field and associated fields are derived in manifestly O(n+1)$\mathrm{O}(n+1)$ covariant or invariant forms. In the large radius limit, these equations reproduce the corresponding field equations defined on the n-dimensional flat space.     

Spontaneous Lorentz violation: Non-Abelian gauge fields as pseudo-Goldstone vector bosons

We argue that non-Abelian gauge fields can be treated as the pseudo-Goldstone vector bosons caused by spontaneous Lorentz invariance violation (SLIV). To this end, the SLIV which evolves in a general Yang–Mills type theory with the nonlinear vector field constraint Tr(AμAμ)=±M²$\mathrm{Tr}({\mathit{A}}_{\mu }{\mathit{A}}^{\mu })=\pm M^2$ (M is a proposed SLIV scale) imposed is considered in detail. Specifically, we show that in a theory with an internal symmetry group G having D   generators not only the pure Lorentz symmetry SO(1,3)$\mathit{SO}(1,3)$, but the larger accidental symmetry SO(D,3D)$\mathit{SO}(D,3D)$ of the SLIV constraint in itself appears to be spontaneously broken as well. As a result, although the pure Lorentz violation on its own still generates only one genuine Goldstone vector boson, the accompanying pseudo-Goldstone vector bosons related to the SO(D,3D)$\mathit{SO}(D,3D)$ breaking also come into play properly completing the whole gauge multiplet of the internal symmetry group G taken. Remarkably, they appear to be strictly massless as well, being protected by the starting non-Abelian gauge invariance of the Yang–Mills theory involved. When expressed in terms of the pure Goldstone vector modes, this theory look essentially nonlinear and contains a plethora of Lorentz and CPT violating couplings. However, they do not lead to physical SLIV effects which turn out to be strictly cancelled in all the lowest order processes considered.     

Towards a Loop Quantum Gravity and Yang–Mills unification

We propose a new method of unifying gravity and the Standard Model by introducing a spin-foam model. We realize a unification between an SU(2)$\mathit{SU}(2)$ Yang–Mills interaction and 3D   general relativity by considering a constrained Spin(4)∼SO(4)$\mathrm{Spin}(4)\sim \mathit{SO}(4)$ Plebanski action. The theory is quantized à la   spin-foam by implementing the analogue of the simplicial constraints for the Spin(4)$\mathrm{Spin}(4)$ symmetry, providing a way to couple Yang–Mills fields to spin-foams. A natural 4D extension of the theory is introduced. We also present a way to recover 2-point correlation functions between the connections as a first way to implement scattering amplitudes between particle states, aiming to connect Loop Quantum Gravity to new physical predictions.     

Exactly solvable models in atomic and molecular physics

We construct integrable generalized models in a systematic way exploring different representations of the gl(N)$\mathit{gl}(N)$ algebra. The models are then interpreted in the context of atomic and molecular physics, most of them related to different types of Bose–Einstein condensates. The spectrum of the models is given through the analytical Bethe ansatz method. We further extend these results to the case of the superalgebra gl(M|N)$\mathit{gl}(M|N)$, providing in this way models which also include fermions.     

Deciphering triply heavy baryons in terms of QCD sum rules

The mass spectra of ground-state triply heavy baryons are systematically unscrambled and computed in QCD sum rules. With a tentative (QQ)–(Q^′)$(\mathit{QQ})\text{–}(Q^{\prime })$ configuration for QQQ^′${\mathit{QQQ}}^{\prime }$, the interpolating currents representing the triply heavy baryons are proposed. Technically, contributions of the operators up to dimension six are included in operator product expansion (OPE). The numerical results are presented in comparison with other theoretical predictions.     

Rational r-matrices,higher rank Lie algebras and integrable proton–neutron BCS models

We study integrable cases of pairing BCS hamiltonians containing several types of fermions. We prove that there exist three classes of such integrable models associated with classical rational r  -matrices and Lie algebras gl(2m)$\mathit{gl}(2m)$, sp(2m)$\mathit{sp}(2m)$ and so(2m)$\mathit{so}(2m)$ correspondingly. We diagonalize the constructed hamiltonians by means of the algebraic Bethe ansatz. In the partial case of two types of fermions (m=2$m=2$) the obtained models may be interpreted as N=Z$N=Z$ proton–neutron integrable models. In particular, in the case of sp(4)$\mathit{sp}(4)$ we recover the famous integrable proton–neutron model of Richardson.     

Rotating Einstein–Maxwell–dilaton black holes in D dimensions

We construct exact charged rotating black holes in Einstein–Maxwell–dilaton theory in D   spacetime dimensions, D?5$D?5$, by embedding the D  -dimensional Myers–Perry solutions in D+1$D+1$ dimensions, and performing a boost with a subsequent Kaluza–Klein reduction. Like the Myers–Perry solutions, these black holes generically possess N=[(D−1)/2]$N=[(D-1)/2]$ independent angular momenta. We present the global and horizon properties of these black holes, and discuss their domains of existence.     

The first application of the Vogel–Fulcher–Tammann equation to biological problem: A new interpretation of the temperature dependent hydrogen exchange rates of the thrombin-binding DNA

The Vogel–Fulcher–Tammann equation, which is widely applied in condensed matter physics, is for the first time applied to analysis of the hydrogen exchange rates of DNA as a function of temperature. The VFT equation, which for hydrogen exchange should read kex=Aexp[−(E/R)/(T−T₀)]$k_{\mathrm{ex}}=A\exp [-(E/R)/(T-T_0)]$, contains a constant temperature T₀$T_0$. When we analyzed the hydrogen exchange rates for the thrombin binding DNA aptamer d  (GGTTGGTGTGGTTGG) as a function of temperature using the VFT equation, we found that T₀$T_0$ happens to be the melting temperature of the DNA. A quantitative relationship is established between the VFT equation and the Arrhenius equation. Under suitable conditions the VFT equation can be reduced to the Arrhenius equation.