The quantum mechanics of perfect fluids

We consider the canonical quantization of an ordinary fluid. The resulting long-distance effective field theory is derivatively coupled, and therefore strongly coupled in the UV. The system however exhibits a number of peculiarities, associated with the vortex degrees of freedom. On the one hand, these have formally a vanishing strong-coupling energy scale, thus suggesting that the effective theory's regime of validity is vanishingly narrow. On the other hand, we prove an analog of Coleman's theorem, whereby the semiclassical vacuum has no quantum counterpart, thus suggesting that the vortex premature strong-coupling phenomenon stems from a bad identification of the ground state and of the perturbative degrees of freedom. Finally, vortices break the usual connection between short distances and high energies, thus potentially impairing the unitarity of the effective theory.Comment: 35 page

Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory

This article is meant as a summary and introduction to the ideas of effective field theory as applied to gravitational systems. Contents: 1. Introduction 2. Effective Field Theories 3. Low-Energy Quantum Gravity 4. Explicit Quantum Calculations 5. ConclusionsComment: 56 pages, 2 figures, JHEP style, Invited review to appear in Living Reviews of Relativit

Effective Theory of a Dynamically Broken Electroweak Standard Model at NLO

We consider the Standard Model as an effective theory at the weak scale $v$ of a generic new strong interaction that dynamically breaks electroweak symmetry at the energy scale $\Lambda\sim$ (few) TeV. Assuming only the minimal field content with the Standard Model fermions and gauge bosons, but without a light Higgs particle, we construct the complete Lagrangian through next-to-leading order, that is, including terms of order $v^2/\Lambda^2$. The systematics behind this expansion is clarified. Although similar to chiral perturbation theory, it is not governed by the dimension of operators alone, but depends in an essential way on the loop expansion. Power-counting formulas are derived that indicate the classes of operators required at the next-to-leading order. The complete set of operators at leading and next-to-leading order is then listed, based on the restrictions implied by the Standard-Model gauge symmetries. We recover the well-known operators discussed in the literature in connection with the electroweak chiral Lagrangian and in similar contexts, but we collect a complete and systematic list of all terms through order $v^2/\Lambda^2$. This includes some operators not discussed in explicit terms before. We also show that a few of the previously considered operators can be eliminated via the equations of motion. As another important result we confirm the known list of dimension-6 operators in the Standard Model with an elementary Higgs doublet, essentially as a special case of our scenario.Comment: 35 pages, 1 figure; references adde

Planck Scale Boundary Conditions and the Higgs Mass

If the LHC does only find a Higgs boson in the low mass region and no other new physics, then one should reconsider scenarios where the Standard Model with three right-handed neutrinos is valid up to Planck scale. We assume in this spirit that the Standard Model couplings are remnants of quantum gravity which implies certain generic boundary conditions for the Higgs quartic coupling at Planck scale. This leads to Higgs mass predictions at the electroweak scale via renormalization group equations. We find that several physically well motivated conditions yield a range of Higgs masses from 127-142 GeV. We also argue that a random quartic Higgs coupling at the Planck scale favors M_H > 150 GeV, which is clearly excluded. We discuss also the prospects for differentiating different boundary conditions imposed for \lambda(M_{pl}) at the LHC. A striking example is M_H = 127\pm 5 GeV corresponding to \lambda(M_{pl})=0, which would imply that the quartic Higgs coupling at the electroweak scale is entirely radiatively generated.Comment: 12 pages, 5 figures; references added and other minor improvements, matches version published in JHE

Proof Theory and Ordered Groups

Ordering theorems, characterizing when partial orders of a group extend to total orders, are used to generate hypersequent calculi for varieties of lattice-ordered groups (l-groups). These calculi are then used to provide new proofs of theorems arising in the theory of ordered groups. More precisely: an analytic calculus for abelian l-groups is generated using an ordering theorem for abelian groups; a calculus is generated for l-groups and new decidability proofs are obtained for the equational theory of this variety and extending finite subsets of free groups to right orders; and a calculus for representable l-groups is generated and a new proof is obtained that free groups are orderable

Two-Point Functions and S-Parameter in QCD-like Theories

We calculated the vector, axial-vector, scalar and pseudo-scalar two-point functions up to two-loop level in the low-energy effective field theory for three different QCD-like theories. In addition we also calculated the pseudo-scalar decay constant $G_M$. The QCD-like theories we used are those with fermions in a complex, real or pseudo-real representation with in general n flavours. These case correspond to global symmetry breaking pattern of $SU(n)_L\times SU(n)_R\to SU(n)_V$, $SU(2n)\to SO(2n)$ or $SU(2n)\to Sp(2n)$. We also estimated the S parameter for those different theories.Comment: 29 page

Vanishing Cosmological Constant by Gravitino-Dressed Compactification of 11D Supergravity

We consider compactifications induced by the gravitino field of eleven dimensional supergravity. Such compactifications are not trivial in the sense that the gravitino profiles are not related to pure bosonic ones by means of a supersymmetry transformation. The basic property of such backgrounds is that they admit $\psi$-torsion although they have vanishing Riemann tensor. Thus, these backgrounds may be considered also as solutions of the teleparallel formulation of supergravity. We construct two classes of solutions, one with both antisymmetric three-form field, gravity and gravitino and one with only gravity and gravitino. In these classes of solutions, the internal space is a parallelized compact manifold, so that it does not inherit any cosmological constant to the external spacetime. The latter turns out to be flat Minkowski in the maximally symmetric case. The elimination of the cosmological constant in the spontaneously compactified supergravity seems to be a generic property based on the trading of the cosmological constant for parallelizing torsion.Comment: 17 pages, no figure

A Rationale for Long-lived Quarks and Leptons at the LHC: Low Energy Flavour Theory

In the framework of gauged flavour symmetries, new fermions in parity symmetric representations of the standard model are generically needed for the compensation of mixed anomalies. The key point is that their masses are also protected by flavour symmetries and some of them are expected to lie way below the flavour symmetry breaking scale(s), which has to occur many orders of magnitude above the electroweak scale to be compatible with the available data from flavour changing neutral currents and CP violation experiments. We argue that, actually, some of these fermions would plausibly get masses within the LHC range. If they are taken to be heavy quarks and leptons, in (bi)-fundamental representations of the standard model symmetries, their mixings with the light ones are strongly constrained to be very small by electroweak precision data. The alternative chosen here is to exactly forbid such mixings by breaking of flavour symmetries into an exact discrete symmetry, the so-called proton-hexality, primarily suggested to avoid proton decay. As a consequence of the large value needed for the flavour breaking scale, those heavy particles are long-lived and rather appropriate for the current and future searches at the LHC for quasi-stable hadrons and leptons. In fact, the LHC experiments have already started to look for them.Comment: 10 pages, 1 figur

Spontaneous Parity Violation in SUSY Strong Gauge Theory

We suggest simple models of spontaneous parity violation in supersymmetric strong gauge theory. We focus on left-right symmetric model and investigate vacuum with spontaneous parity violation. Non-perturbative effects are calculable in supersymmetric gauge theory, and we suggest two new models. The first model shows confinement, and the second model has a dual description of the theory. The left-right symmetry breaking and electroweak symmetry breaking are simultaneously occurred with the suitable energy scale hierarchy. The second model also induces spontaneous supersymmetry breaking.Comment: 14 page

Vacuum stability, neutrinos, and dark matter

Motivated by the discovery hint of the Standard Model (SM) Higgs mass around 125 GeV at the LHC, we study the vacuum stability and perturbativity bounds on Higgs scalar of the SM extensions including neutrinos and dark matter (DM). Guided by the SM gauge symmetry and the minimal changes in the SM Higgs potential we consider two extensions of neutrino sector (Type-I and Type-III seesaw mechanisms) and DM sector (a real scalar singlet (darkon) and minimal dark matter (MDM)) respectively. The darkon contributes positively to the $\beta$ function of the Higgs quartic coupling $\lambda$ and can stabilize the SM vacuum up to high scale. Similar to the top quark in the SM we find the cause of instability is sensitive to the size of new Yukawa couplings between heavy neutrinos and Higgs boson, namely, the scale of seesaw mechanism. MDM and Type-III seesaw fermion triplet, two nontrivial representations of $SU(2)_{L}$ group, will bring the additional positive contributions to the gauge coupling $g_{2}$ renormalization group (RG) evolution and would also help to stabilize the electroweak vacuum up to high scale.Comment: 18 pages, 15 figures; published versio