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Register a new userThe mixed $0$-form/$1$-form anomaly in Hilbert space: pouring new wine into old bottles
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We study four-dimensional gauge theories with arbitrary simple gauge group with $1$-form global center symmetry and $0$-form parity or discrete chiral symmetry. We canonically quantize on $mathbb{T}^3$, in a fixed background field gauging the $1$-form symmetry. We show that the mixed $0$-form/$1$-form t Hooft anomaly results in a central extension of the global-symmetry operator algebra. We determine this algebra in each case and show that the anomaly implies degeneracies in the spectrum of the Hamiltonian at any finite-size torus. We discuss the consistency of these constraints with both older and recent semiclassical calculations in $SU(N)$ theories, with or without adjoint fermions, as well as with their conjectured infrared phases.
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We show that the Standard Model (SM) Higgs Lagrangian is identical to the nonlinear realization of both the scale and chiral symmetries (scale-invariant nonlinear sigma model), and is further gauge equivalent to the scale-invariant Hidden Local Symmetry (HLS) model having possible new vector bosons as the HLS gauge bosons with scale-invariant mass: SM Higgs is nothing but a (pseudo) dilaton. The effective theory of the walking technicolor has precisely the same type of the scale-invariant nonlinear sigma model, thus further having the scale-invariant HLS gauge bosons (technirhos, etc.). The technidilaton mass M_phi comes from the trace anomaly, which yields M_phi^2 F_phi^2 simeq (2.5)^2 [(8/N_F)(4/N_C)] v^4 via PCDC, in the underlying walking SU(N_C) gauge theory with N_F massless flavors, where F_phi is the decay constant and v=246 GeV. This implies F_phi simeq 5 v for M_phi simeq 125 GeV simeq v/2 in the one-family walking technicolor model (N_F=8, N_C=4), in good agreement with the current LHC Higgs data. In the anti-Veneziano limit, N_C rightarrow infty, with N_C alpha= fixed and N_F/N_C= fixed (gg 1), we have a result: M_phi^2/v^2sim M_phi^2/F_phi^2 sim 1/(N_F N_C) rightarrow 0. Then the technidilaton is a naturally light composite Higgs out of the strongly coupled conformal dynamics, with its couplings even weaker than the SM Higgs.
The rare decay $Btopiell^+ell^-$ arises from $bto d$ flavor-changing neutral currents and could be sensitive to physics beyond the Standard Model. Here, we present the first $ab$-$initio$ QCD calculation of the $Btopi$ tensor form factor $f_T$. Together with the vector and scalar form factors $f_+$ and $f_0$ from our companion work [J. A. Bailey $et~al.$, Phys. Rev. D 92, 014024 (2015)], these parameterize the hadronic contribution to $Btopi$ semileptonic decays in any extension of the Standard Model. We obtain the total branching ratio ${text{BR}}(B^+topi^+mu^+mu^-)=20.4(2.1)times10^{-9}$ in the Standard Model, which is the most precise theoretical determination to date, and agrees with the recent measurement from the LHCb experiment [R. Aaij $et~al.$, JHEP 1212, 125 (2012)]. Note added: after this paper was submitted for publication, LHCb announced a new measurement of the differential decay rate for this process [T. Tekampe, talk at DPF 2015], which we now compare to the shape and normalization of the Standard-Model prediction.
We investigate the modeling capabilities of sets of coupled classical harmonic oscillators (CHO) in the form of a modeling game. The application of simple but restrictive rules of the game lead to conditions for an isomorphism between Lie-algebras and real Clifford algebras. We show that the correlations between two coupled classical oscillators find their natural description in the Dirac algebra and allow to model aspects of special relativity, inertial motion, electromagnetism and quantum phenomena including spin in one go. The algebraic properties of Hamiltonian motion of low-dimensional systems can generally be related to certain types of interactions and hence to the dimensionality of emergent space-times. We describe the intrinsic connection between phase space volumes of a 2-dimensional oscillator and the Dirac algebra. In this version of a phase space interpretation of quantum mechanics the (components of the) spinor wave-function in momentum space are abstract canonical coordinates, and the integrals over the squared wave function represents second moments in phase space. The wave function in ordinary space-time can be obtained via Fourier transformation. Within this modeling game, 3+1-dimensional space-time is interpreted as a structural property of electromagnetic interaction. A generalization selects a series of Clifford algebras of specific dimensions with similar properties, specifically also 10- and 26-dimensional real Clifford algebras.
Recently introduced generalized global symmetries have been useful in order to understand non-perturbative aspects of quantum field theories in four and lower dimensions. In this paper we focus on 1-form symmetries of weakly coupled 6d supersymmetric gauge theories coupled to tensor multiplets. We study their interplay with large gauge transformations for dynamical tensor fields. In a non-trivial background for the global 1-form symmetry, this leads to an ambiguity of the effective field theory partition function. This anomaly is eliminated by the inclusion of BPS strings. However, the non-trivial 1-form background can induce fractional string charges which are not compatible with Dirac quantization, and hence the symmetry is absent. The anomalous term therefore serves as a tool to detect whether the discrete 1-form symmetries are realized, which we demonstrate in explicit examples originating from string compactifications. We also corroborate this by finding that a non-trivial ambiguity is related to states which explicitly break the global 1-form symmetry, which appear as generally massive excitations of the 6d BPS strings. For 6d theories consistently coupled to gravity, this ambiguity of the partition function hints at the presence of a symmetry breaking tower of states. When the ambiguity is absent, the F-theory realization of the theories points to the gauging of the 1-form symmetries via the presence of non-trivial Mordell--Weil torsion.
We present the N_f=2+1 clover fermion lattice QCD calculation of the nucleon strangeness form factors. We evaluate disconnected insertions using the Z(4) stochastic method, along with unbiased subtractions from the hopping parameter expansion. We find that increasing the number of nucleon sources for each configuration improves the signal significantly. We obtain G_M^s(0) = -0.017(25)(07), where the first error is statistical, and the second is the uncertainties in Q^2 and chiral extrapolations. This is consistent with experimental values, and has an order of magnitude smaller error.
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