arXiv subjects
Publications and source records attributed to Taichiro Kugo.
The Wilson effective action for general Yang-Mills gauge theory is shown to satisfy the usual form of Batalin-Vilkovisky (BV) master equation, despite that a momentum cutoff apparently breaks the gauge invariance. In the case of Abelian gauge theory, in particular, it actually deduces the Ward-Takahashi identity for Wilson action recently derived by Sonoda.
The recently observed pentaquark baryons $Θ^{+}$ and $Ξ^{--}$ are studied in the dual gravity theory of QCD. By developing a general formulation useful for studying the branched string web in a curved space, simple mass formulae of the pentaquark baryons are derived in the Maldacena prototype model for supersymmetric QCD and a more realistic model for ordinary QCD. Even though the approximations adopted here in deriving these formulae are extremely naive, the predicted values of the masses do not differ significantly from their experimental values. We thus conclude that this approach is promising for the purpose of obtaining a description of the observed masses of pentaquarks and of their extremely narrow decay widths. With the aim of constructing more reliable mass formulae, a preliminary sketch is given of how spin, the hyperfine interaction and parity are considered in the string picture.
Under the assumptions that 1) the quark/lepton mass matrices take Froggatt-Nielsen's factorized power form λ^{ψ_i+ψ_j} with anomalous U(1) charges ψ_i, and 2) the U(1) charges ψ_i respect the SU(5) GUT structure, we show that the quark mass data and the mass-squared difference ratio of solar and atmospheric neutrinos, as inputs, necessarily imply that both the 1-2 and 2-3 mixings in the MNS matrix U_{MNS} are large. This analysis also gives a prediction that U_{e3}\equiv (U_{MNS})_{13} is of order λ\sim (0.1 - 0.5). We also add an argument that E_6 GUT is favored.
Under the assumptions that 1) the quark/lepton mass matrices take Froggatt-Nielsen's factorized power form λ^{ψ_i+ψ_j} with anomalous U(1) charges ψ_i, and 2) the U(1) charges ψ_i respect the SU(5) GUT structure, we show that the quark mass data necessarily implies the large 2-3 mixing in the MNS mixing matrix U_{MNS}. If we further add the data of the mass squared difference ratio of solar and atmospheric neutrinos, then, it implies that the 1-2 mixing in U_{MNS} is also large, so explaining the bi-large mixing. This analysis also gives a prediction that U_{e3}\equiv(U_{\rm MNS})_{13} should be of order λ\sim (0.1 - 0.5).
The idea to have Higgs doublets as pseudo Nambu-Goldstone (PsNG) multiplet is examined in the framework of supersymmetric E_6 unified theory. We show that extra PsNG multiplets other than the expected Higgs doublets necessarily appear in the E_6 case. If we demand that the extra PsNG multiplets neither disturb the gauge coupling unification nor make the color gauge coupling diverge before unification occurs, only possibility for the extra PsNG is 10+\bar{10} of SU(5). This is realized when the symmetry breaking E_6 \to SO(10) occurs in the ϕ(27)+ϕ(\bar{27}) sector while E_6 \to SU(4)_C\times SU(2)_L\times U(1)\times U(1) in the Σ(78) sector. The existence of 10+\bar{10} multiplets with mass around 1 TeV is therefore a prediction of this E_6 PsNG scenario. Implication of their existence on the proton decay is also discussed.
Superconformal tensor calculus on an orbifold S^1/Z_2 is given in five-dimensional (5D) spacetime. The four-dimensional superconformal Weyl multiplet and various matter multiplets are induced on the boundary planes from the 5D supermultiplets in the bulk. We identify those induced 4D supermultiplets and clarify a general method for coupling the bulk fields to the matter fields on the boundaries in a superconformal invariant manner.
An off-shell formulation is given for the ``supersymmetry in singular spaces'' which has recently been developed in an on-shell formalism by Bergshoeff, Kallosh and Van Proeyen using supersymmetry singlet `coupling constant' field and 4-form multiplier field in five-dimensional space-time. We present this formulation for a general supergravity-Yang-Mills-hypermultiplet coupled system compactified on an orbifold $S^1/Z_2$. Relations between the bulk cosmological constant and brane tensions of the boundary planes are discussed.
A novel relation is found which gives the 2-3 lepton mixing angle in terms of quark masses and CKM mixing: \tanθ_{μτ}=(m_b/m_s)V_{cb}. This relation, which is remarkably in good agreement with the quark data and the large lepton mixing recently observed, is a kind of SO(10) GUT relation similar to the celebrated bottom-tau mass ratio in SU(5). The GUT models in which this relation hold should have a `twisted SO(10)' structure between the second and third generations, in order to really explain the large lepton mixing, or equivalently, the right-hand side of the relation.
We investigate a possibility that our four-dimensional world is a brane-like object embedded in a higher dimensional spacetime. In such a situation, the transverse coordinates of the brane become the Nambu-Goldstone bosons which appear as a result of spontaneous breaking of the translation symmetry. We determine the form of the effective action of the system, finding the explicit form of the vierbein induced on the brane in terms of the Nambu-Goldstone boson variables and the bulk vielbein. As was pointed out in the previous paper, the Kaluza-Klein mode couplings are suppressed by the effect of the brane fluctuation and the suppression is stronger if the brane tension is smaller. However, we here show that the brane tension cannot be arbitrarily small since the inverse of the brane tension gives the coupling constant of the Nambu-Goldstone bosons. A rather stringent bound is obtained for the brane tension and the fundamental (`string') scale from the consideration of the cooling process of the supernova.
We show that the neutrino masses with large mixing between ν_μand ν_τare naturally reproduced in a supersymmetric E_6 grand unification model with an anomalous U(1)_X symmetry. We propose a simple scenario which incorporates a novel mechanism called `E-twisting' by which all the characteristic features of the fermion mass matrices, not only the quark/lepton's Dirac masses but also the neutrino's Majorana masses, can be well reproduced despite all the members in 27 of each generation are assigned a common U(1)_X charge.
We calculate one-loop 2-point tachyon amplitudes in unoriented open-closed string field theory, and determine all the coupling constants of the interaction vertices in the theory. It is shown that the planar, nonplanar and nonorientable amplitudes are all reproduced correctly, and nontrivial consistencies between the determined coupling constants are observed. The necessity for the gauge group to be SO(2^{13}=8192) is also reconfirmed.
We present the full action for the unoriented open-closed string field theory which is based on the α=p^+ HIKKO type vertices. The BRS invariance of the action is proved up to the terms which are expected to cancel the anomalous one-loop contributions. This implies that the system is invariant under the gauge transformations with open and closed string field parameters up to the anomalies.
The generalized gluing and resmoothing theorem originally proved by LeClair, Peskin and Preitschopf, gives a powerful formula for the fused vertex obtained by contracting any two vertices in string field theories. Although the theorem is naturally expected to hold for the vertices at any loop level, the original proof was restricted to the vertices at tree level. Here we present a simplified proof for the tree level theorem and then prove explicitly the extended version at one-loop level. We also find that a non-trivial sign factor, which depends on the string states to be contracted, appears in the theorem. This sign factor turns out to be essential for reproducing correctly the conformal field theory correlation function on the torus.
The string field theory for unoriented open-closed string mixed system is constructed up to quadratic order based on the joining-splitting type vertices. The gauge invariance with closed string transformation parameter is proved. The infinity cancellation mechanism between disk and projective plane amplitudes plays an essential role for the gauge invariance of the theory.
The ratio Z_1/Z_3 of vertex and wave-function renormalization factors, which is universal (i.e., matter-independent), is shown to equal 1+u which gives the residue of the scalar pole $\propto p_μp_ν/p^2$ of 2-point function < D_μc D_ν\bar c >. This relation is interesting since 1+u=0 has been known to give a sufficient condition for color confinement. We also give an argument that, when 1+u=0 holds, it will be realized by the disappearance of the massless gauge boson pole and is related with the restoration of a certain ``local gauge symmetry" as was discussed by Hata. (Talk given at International Symposium on BRS Symmetry, Sept.~18 -- 22, 1995, Kyoto.)
A systematic method is given for obtaining consistent approximations to the Schwinger-Dyson(SD) and Bethe-Salpeter(BS) equations which maintain the external gauge invariance. We show that for any order of approximation to the SD equation there is a corresponding approximation to the BS equations such that the solutions to those equations satisfy the Ward-Takahashi identities of the external gauge symmetry. This formulation also clarifies the way how we can calculate the Green functions of current operators in a consistent manner with the gauge invariance and the axial anomaly. We show which type of diagrams for the $π^0\rightarrowγγ$ amplitude using the pion BS amplitude give result consistent with the low-energy theorem. An interesting phenomenon is observed in the ladder approximation that the low energy theorem is saturated by the zeroth order terms in the external momenta of the pseudoscalar BS amplitude and the vector vertex functions.
We develop the improved ladder approximation to QCD in order to apply it to the heavy quark mesons. The resulting Bethe-Salpeter equation is expanded in powers of the inverse heavy quark mass 1/M, and is shown to be consistent with the heavy quark spin symmetry. We calculate numerically the universal leading order BS amplitude for heavy pseudoscalar and vector mesons, and use this to evaluate the Isgur-Wise function and the decay constant F_B. The resulting Isgur-Wise function predicts a large charge radius, rho^2 = 1.8 - 2.0, which when fitted to the ARGUS data corresponds to the value Vcb = .044 - .050 for the Kobayashi-Maskawa matrix element.
We prove to all orders of the loop expansion the low energy theorems of hidden local symmetries in four-dimensional nonlinear sigma models based on the coset space $G/H$, with $G$ and $H$ being arbitrary compact groups. Although the models are non-renormalizable, the proof is done in an analogous manner to the renormalization proof of gauge theories and two-dimensional nonlinear sigma models by restricting ourselves to the operators with two derivatives (counting a hidden gauge boson field as one derivative), i.e., with dimension 2, which are the only operators relevant to the low energy limit. Through loop-wise mathematical induction based on the Ward-Takahashi identity for the BRS symmetry, we solve renormalization equation for the effective action up to dimension-2 terms plus terms with the relevant BRS sources. We then show that all the quantum corrections to the dimension-2 operators, including the finite parts as well as the divergent ones, can be entirely absorbed into a re-definition (renormalization) of the parameters and the fields in the dimension-2 part of the tree-level Lagrangian.