I review the generating function for quantum-statistical mechanics, known as the Feynman-Vernon influence functional, the decoherence functional, or the Schwinger-Keldysh path integral. I describe a probability-conserving $ivarepsilon$ prescription f
rom a path-integral implementation of Lindblad evolution. I also explain how to generalize the formalism to accommodate out-of-time-ordered correlators (OTOCs), leading to a Larkin-Ovchinnikov path integral. My goal is to provide step-by-step calculations of path integrals associated to the harmonic oscillator.
I generalize the Dray-t Hooft gravitational shockwave to the Kerr-AdS background.
We present an exact solution of Einsteins equation that describes the gravitational shockwave of a massless particle on the horizon of a Kerr-Newman black hole. The backreacted metric is of the generalized Kerr-Schild form and is Type II in the Petro
v classification. We show that if the background frame is aligned with shear-free null geodesics, and if the background Ricci tensor satisfies a simple condition, then all nonlinearities in the perturbation will drop out of the curvature scalars. We make heavy use of the method of spin coefficients (the Newman-Penrose formalism) in its compacted form (the Geroch-Held-Penrose formalism).
We exploit a recent advance in the study of topological superconductors to propose a solution to the family puzzle of particle physics in the context of SO(18) (or more correctly, Spin(18)) grand unification. We argue that Yukawa couplings of interme
diate strength may allow the mirror matter and extra families to decouple at arbitrarily high energies. As was clear from the existing literature, we have to go beyond the Higgs mechanism in order to solve the family puzzle. A pattern of symmetry breaking which results in the SU(5) grand unified theory with horizontal or family symmetry USp(4) = Spin(5) (or more loosely, SO(5)) leaves exactly three light families of matter and seems particularly appealing. We comment briefly on an alternative scheme involving discrete non-abelian family symmetries. In a few lengthy appendices we review some of the pertinent condensed matter theory.
I study the prospect of generating mass for symmetry-protected fermions without breaking the symmetry that forbids quadratic mass terms in the Lagrangian. I focus on 1+1 spacetime dimensions in the hope that this can provide guidance for interacting
fermions in 3+1 dimensions. I first review the SO(8) Gross-Neveu model and emphasize a subtlety in the triality transformation. Then I focus on the m = 0 manifold of the SO(7) Kitaev-Fidkowski model. I argue that this theory exhibits a phenomenon similar to parity doubling in hadronic physics, and this leads to the conclusion that the fermion propagator vanishes when p = 0. I also briefly explore a connection between this model and the two-channel, single-impurity Kondo effect. This paper may serve as an introduction to topological superconductors for high energy theorists, and perhaps as a taste of elementary particle physics for condensed matter theorists.
The A4 x U(1) flavor model of He, Keum, and Volkas is extended to provide a minimal modification to tribimaximal mixing that accommodates a nonzero reactor angle theta13 ~ 0.1. The sequestering problem is circumvented by forbidding superheavy scales
and large coupling constants which would otherwise generate sizable RG flows. The model is compatible with (but does not require) a stable or metastable dark matter candidate in the form of a complex scalar field with unit charge under a discrete subgroup Z4 of the U(1) flavor symmetry.
We study the LHC phenomenology of a general class of Private Higgs (PH) models, in which fermions obtain their masses from their own Higgs doublets with $op(1)$ Yukawa couplings, and the mass hierarchy is translated into a dynamical chain of vacuum e
xpectation values. This is accomplished by introducing a number of light gauge-singlet scalars, the darkons, some of which could play the role of dark matter. These models allow for substantial modifications to the decays of the lightest Higgs boson, for instance through mixing with TeV-scale PH fields and light darkons: the simplest version of the model predicts the ratios of partial widths to satisfy $G(h to VV^*)_{text{PH}}/G(h to VV^*)_{text{SM}} approx G(h to gg)_{text{PH}}/G(h to gg)_{text{SM}} leq 1$ and $G(h to bbar b)_{text{PH}}/G(h to bbar b)_{text{SM}} sim op(1)$, where the inequalities are saturated only in the absence of Higgs mixing with light darkons. An extension of the model proposed previously for generating nonzero neutrino masses can also contribute substantially to $h to gg$ without violating electroweak precision constraints. If the Higgs coupling to fermions is found to deviate from the Standard Model (SM) expectation, then the PH model may be a viable candidate for extending the SM.
It is consistent with the measurement of theta_13 ~ 0.15 by Daya Bay to suppose that, in addition to being unitary, the neutrino mixing matrix is also almost hermitian, and thereby only a small perturbation from diag(+1,-1,-1) in a suitable basis. We
suggest this possibility simply as an easily falsifiable ansatz that has not already been studied, as well as to offer a potentially useful means of organizing the experimental data. We explore the phenomenological implications of this ansatz and parametrize one type of deviation from the leading order relation |V_e3| approx |V_tau 1|. We also emphasize the group-invariant angle between orthogonal matrices as a means of comparing to data. The discussion is purely phenomenological, without any attempt to derive the condition V{dag} approx V from a fundamental theory.
We use the discrete group Sigma(81) = (Z_3 x Z_3 x Z_3)rtimes Z_3 to explore a particular region of parameter space in the Private Higgs model. In doing so we suggest a relation among the off-diagonal entries of the neutrino mass matrix and a possibl
e explanation for the muon magnetic moment anomaly, a_mu^{exp}-a_mu^{SM} ~ 10^{-9}. We predict three new nearly degenerate Higgs doublets with masses of order ~ 500 GeV to ~ 1 TeV, and three nearly degenerate SM-singlet TeV-scale neutrinos. The largest scale in the model is ~ 10 TeV, so there is no severe hierarchy problem. The appendix is devoted to the group theory of Sigma(81).
Motivated by the possibility that the amplitude for neutrinoless double beta decay may be much smaller than the planned sensitivity of future experiments, we study ansatze for the neutrino mass matrix with $M_{ee} = 0$. For the case in which CP is co
nserved, we consider two classes of real-valued mass matrices: Class I defined by $|M_{emu}| = |M_{etau}|$, and Class II defined by $|M_{mumu}| = |M_{tautau}|$. The important phenomenological distinction between the two is that Class I permits only small values of $V_{e3}$ up to $sim 0.03$, while Class II admits large values of $V_{e3}$ up to its empirical upper limit of 0.22. Then we introduce CP-violating complex phases into the mass matrix. We show that it is possible to have tribimaximal mixing with $M_{ee} = 0$ and $|M_{mutau}| = |M_{mumu}| = |M_{tautau}|$ if the Majorana phase angles are $pmpi/4$. Alternatively, for smaller values of $|M_{mutau}| = |M_{mumu}| = |M_{tautau}|$ it is possible to obtain $|V_{e3}| sim 0.2$ and generate relatively large CP-violating amplitudes. To eliminate phase redundancy, we emphasize rephasing any mass matrix with $M_{ee} = 0$ into a standard form with two complex phases. The discussion alternates between analytical and numerical but remains purely phenomenological, without any attempt to derive mass matrices from a fundamental theory.
