119978808
AFFINE (TWO-LOOP) WZNW MODEL, REDUCTION AND SPONTANEOUS BREAKDOWN OF CONFORMAL SYMMETRY
A large theory—the affine (two-loop) WZNW theory, which is universal in the sense that (at least classically) conformal and integrable models may be considered as its various reductions, has been proposed in our recent papers with Bonora and Martellini. In this letter we study a different Hamiltonian reduction (named as type III reduction in the text) of the affine (two-loop) WZNW model and discuss the integrability property of the reduced model. By a BRST analysis, we elaborate on a previously introduced idea regarding integrable systems as spontaneously conformal-symmetry-broken versions of CFTs.
119694191
Construction of basis vectors for symmetric irreducible representations of O(5) $ \supset$ O(3)
Abstract.A recursive method for the construction of symmetric irreducible representations of $ O(2l+1)$ in the $ O(2l+1)\supset O(3)$ basis for identical boson systems is proposed. The formalism is realized based on the group chain $ U(2l+1)\supset U(2l-1)\otimes U(2)$ , of which the symmetric irreducible representations are simply reducible. The basis vectors for symmetric irreducible representations of the $ O(2l+1)\supset O(2l-1)\otimes U(1)$ can easily be constructed from those of U(2l + 1) $ \supset$U(2l - 1) ⊗ U(2) $ \supset$O(2l - 1) ⊗ U(1) with no l -boson pairs, namely with the total boson number exactly equal to the seniority number in the system, from which one can construct symmetric irreducible representations of $ O(2l+1)$ in the $ O(2l-1)\otimes U(1)$ basis when all symmetric irreducible representations of O(2l - 1) are known. As a starting point, basis vectors of symmetric irreducible representations of O(5) are constructed in the $ O_{1}(3)\otimes U(1)$ basis, where $ O_{1}(3)\equiv O(2l-1)$ , when l = 2 , which is generated not by the angular momentum operators of the d -boson system, but by the operators constructed from d -boson creation (annihilation) operators $ d^{\dagger}_{\mu}$ ( $ d_{\mu}$ with $ \mu=1$ , 0, -1 . Matrix representations of $ O(5)\supset O_{1}(3)\otimes U(1)$ , together with the elementary Wigner coefficients, are presented. After the angular momentum projection, a three-term relation in determining the expansion coefficients of the $ O(5)\supset O(3)$ basis vectors, where the O(3) group is generated by the angular momentum operators of the d -boson system, in terms of those of $ O_{1}(3)\otimes U(1)$ is derived. The eigenvectors of the projection matrix with zero eigenvalues constructed according to the three-term relation completely determine the basis vectors of $ O(5)\supset O(3)$ . Formulae for evaluating the elementary Wigner coefficients of $ O(5)\supset O(3)$ are derived explicitly. Analytical expressions of some elementary Wigner coefficients of $ O(5)\supset O(3)$ for the coupling $ (\tau 0)\otimes(1 0)$ with resultant angular momentum quantum number L = 2$ \tau$ + 2 - k for $ k=0,2,3,\ldots,6$ with a multiplicity 2 case for k = 6 are presented.
1264030
Elliptic Gaudin models and elliptic KZ equations
The Gaudin models based on the face-type elliptic quantum groups and the XYZ Gaudin models are studied. The Gaudin model Hamiltonians are constructed and are diagonalized by using the algebraic Bethe ansatz method. The corresponding face-type Knizhnik–Zamolodchikov equations and their solutions are given.
2107479
Local Quasitriangular Hopf Algebras
We find a new class of Hopf algebras, local quasitriangular Hopf algebras, which generalize quasitriangular Hopf algebras. Using these Hopf algebras, we obtain solutions of the Yang-Baxter equation in a systematic way. The category of modules with finite cycles over a local quasitriangular Hopf algebra is a braided tensor category.
121731174
Some algebraic identities in anomalous gauge theories
Some useful algebraic relations between the anomaly of Dmu Jmu and anomalous commutators are derived using only the canonical commutators and the equation of motion. Their applications are discussed.
17047722
Infinite Families of Gauge-Equivalent R-Matrices and Gradations of Quantized Affine Algebras
Associated with the fundamental representation of a quantum algebra such as Uq(A1) or Uq(A2), there exist infinitely many gauge-equivalent R-matrices with different spectralparameter dependences. It is shown how these can be obtained by examining the infinitely many possible gradations of the corresponding quantum affine algebras, such as and , and explicit formulae are obtained for those two cases. Spectral-dependent similarity (gauge) transformations relate the R-matrices in different gradations, Nevertheless, the choice of gradation can be physically significant, as is illustrated in the case of quantum affine Toda field theories.
15207037
Global structure of curves from generalized unitarity cut of three-loop diagrams
A bstractThis paper studies the global structure of algebraic curves defined by generalized unitarity cut of four-dimensional three-loop diagrams with eleven propagators. The global structure is a topological invariant that is characterized by the geometric genus of the algebraic curve. We use the Riemann-Hurwitz formula to compute the geometric genus of algebraic curves with the help of techniques involving convex hull polytopes and numerical algebraic geometry. Some interesting properties of genus for arbitrary loop orders are also explored where computing the genus serves as an initial step for integral or integrand reduction of three-loop amplitudes via an algebraic geometric approach.
119109271
Type II Seesaw at LHC: The Roadmap
In this Letter we revisit the type-II seesaw mechanism based on the addition of a weak triplet scalar to the standard model. We perform a comprehensive study of its phenomenology at the LHC energies, complete with the electroweak precision constraints. We pay special attention to the doubly-charged component, object of collider searches for a long time, and show how the experimental bound on its mass depends crucially on the particle spectrum of the theory. Our study can be used as a roadmap for future complete LHC studies.
121435769
Phase Structure of Strange Matter in a Non-topological Soliton Model
A non-topological soliton model with strange quarks is suggested to investigate the phase structure of strange matter. The results are qualitatively in agreement with that obtained by MIT bag model provided the ratio of coupling constants of different quarks to soliton scalar field chi(sigma) = g(s sigma)/g(q sigma) larger than a critical value chi(c) similar to 0.86, but as chi(sigma) gets smaller than chi(c), the phase structure may change.
119263398
Multi-loop Integrand Reduction with Computational Algebraic Geometry
We discuss recent progress in multi-loop integrand reduction methods. Motivated by the possibility of an automated construction of multi-loop amplitudes via generalized unitarity cuts we describe a procedure to obtain a general parameterisation of any multi-loop integrand in a renormalizable gauge theory. The method relies on computational algebraic geometry techniques such as Grobner bases and primary decomposition of ideals. We present some results for two and three loop amplitudes obtained with the help of the MACAULAY2 computer algebra system and the Mathematica package BASISDET.
118866595
Atmospheric Neutrino Mixing and b → s Transitions: Testing Lopsided SO(10) Flavor Structure in B physics
We point out that the correlation between the large atmospheric neutrino mixing and the b! s transition, if exists, comes from the lopsided flavor structure in SO(10) grand unification theory. We suggest testing the correlation by studying the deviation of SKS and S�'KS from the standard model predictions along with the constraints fromMBS and b! s in a realistic SO(10) model with lopsided flavor structure. We find a specific correlation between SKS and S�'KS that is intrinsic to the lopsided structure and discuss how to confirm or rule out this flavor pattern by the more accurate measurements of these CP violation quantities in B decay. The standard model (SM), although has passed many precision experimental tests, still has a number of out- standing problems which beg for a more fundamental the- ory. In terms of phenomenology, there are many places to test the more fundamental theory and, quite often, it is not one piece of phenomenology but a specific pattern of many pieces of phenomenology that fulfils this job. Neutrino oscillation clearly indicates the beyond SM physics in that it violates the accidental symmetry Le,µ,� of SM lepton flavor. Moreover, the tiny neutrino masses can be most naturally explained by the seesaw mech- anism (1), indicating the Majorana nature of neutrinos that leads to violation of another accidental symmetry B − L of SM at a very high scale close to the grand unification theory (GUT) scale. For this reason, study- ing neutrino oscillation in the GUT framework becomes particularly interesting. In SO(10) GUT, quarks and leptons are unified into a single 16 multiplet, yet experimental data shows that the 2-3 (generation) mixing is dramatically different in the quark and lepton sectors. While the quark mixing an- gle θ CKM is around 0.04, the lepton mixing angle θ PMNS (atmospheric mixing angle) is quite large and could be a maximum of π/4. This difference can be rather naturally explained by the lopsidedness in the 2-3 sector of mass matrices of down-type quarks and charged leptons: