Conformal Sector Research Articles

Searching for modified gravity: a conformal sector?

We conjecture that any modification of general relativity can be studied by the minimal geometric deformation approach provided that such modification can be represented by a traceless energy-momentum tensor.

750 GeV diphotons: implications for supersymmetric unification II

Perturbative supersymmetric gauge coupling unification is possible in six theories where complete SU(5) TeV-scale multiplets of vector matter account for the size of the reported $750~{\rm GeV}$ diphoton resonance, interpreted as a singlet multiplet $S = (s+ia)/\sqrt{2}$. One of these has a full generation of vector matter and a unified gauge coupling $\alpha_G \sim 1$. The diphoton signal rate is enhanced by loops of vector squarks and sleptons, especially when the trilinear $A$ couplings are large. If the $SH_u H_d$ coupling is absent, both $s$ and $a$ can contribute to the resonance, which may then have a large apparent width if the mass splitting from $s$ and $a$ arises from loops of vector matter. The width depends sensitively on $A$ parameters and phases of the vector squark and slepton masses. Vector quarks and/or squarks are expected to be in reach of the LHC. If the $SH_uH_d$ coupling is present, $a$ leads to a narrow diphoton resonance, while a second resonance with decays $s \rightarrow hh, W^+ W^-,ZZ$ is likely to be discovered at future LHC runs. In some of the theories a non-standard origin or running of the soft parameters is required, for example involving conformal hidden sector interactions.

A proper fixed functional for four-dimensional Quantum Einstein Gravity

Realizing a quantum theory for gravity based on Asymptotic Safety hinges on the existence of a non-Gaussian fixed point of the theory’s renormalization group flow. In this work, we use the functional renormalization group equation for the effective average action to study the fixed point underlying Quantum Einstein Gravity at the functional level including an infinite number of scale-dependent coupling constants. We formulate a list of guiding principles underlying the construction of a partial differential equation encoding the scale-dependence of f(R)-gravity. We show that this equation admits a unique, globally well-defined fixed functional describing the non-Gaussian fixed point at the level of functions of the scalar curvature. This solution is constructed explicitly via a numerical double-shooting method. In the UV, this solution is in good agreement with results from polynomial expansions including a finite number of coupling constants, while it scales proportional to R2, dressed up with non-analytic terms, in the IR. We demonstrate that its structure is mainly governed by the conformal sector of the flow equation. The relation of our work to previous, partial constructions of similar scaling solutions is discussed.

Supersymmetry hidden in the continuum

We study models where the superpartners of the ordinary particles have continuous spectra rather than being discrete states, which can occur when the supersymmetric standard model is coupled to an approximately conformal sector. We show that when superpartners that are well into the continuum are produced at a collider, they tend to have long decay chains that step their way down through the continuum emitting many fairly soft standard model particles along the way, with a roughly spherical energy distribution in the center of mass frame.

Superconformal Technicolor

In supersymmetric theories with a strong conformal sector, soft supersymmetry breaking at the TeV scale naturally gives rise to confinement and chiral symmetry breaking at the same scale. We consider two such scenarios, one where the strong dynamics induces vacuum expectation values for elementary Higgs fields, and another where the strong dynamics is solely responsible for electroweak symmetry breaking. In both cases, the mass of the Higgs boson can exceed the LEP bound without tuning, solving the supersymmetry naturalness problem. A good precision electroweak fit can be obtained, and quark and lepton masses are generated without flavor-changing neutral currents. In addition to standard supersymmetry signals, these models predict production of multiple heavy standard model particles (t, W, Z, and b) from decays of resonances in the strong sector.

Superconformal technicolor: Models and phenomenology

In supersymmetric theories with a strong conformal sector, soft supersymmetry breaking naturally gives rise to confinement and chiral symmetry breaking in the strong sector at the TeV scale. We construct and analyze models where such a sector dynamically breaks electroweak symmetry, and take the first steps in studying their phenomenology. We consider two scenarios, one where the strong dynamics induces vacuum expectation values for elementary Higgs fields, and another where the strong dynamics is solely responsible for electroweak symmetry breaking. In both cases there is no fine-tuning required to explain the absence of a Higgs boson below the LEP bound, solving the supersymmetry naturalness problem. Quark and lepton masses arise from conventional Yukawa couplings to elementary Higgs bosons, so there are no additional flavor-changing effects associated with the strong dynamics. A good precision electroweak fit can be obtained because the strong sector is an $SU(2)$ gauge theory with one weak doublet, and has adjustable parameters that control the violation of custodial symmetry. In addition to the standard supersymmetry signals, these models predict production of multiple heavy standard model particles ($t$, $W$, $Z$, and $b$) from decays of resonances in the strong sector. The strong sector has no approximate parity symmetry, so $WW$ scattering is unitarized by states that can decay to $WWW$ as well as $WW$.

Electroweak symmetry breaking in the DSSM

We study the theoretical and phenomenological consequences of modifying the Kahler potential of the MSSM two Higgs doublet sector. Such modifications naturally arise when the Higgs sector mixes with a quasi-hidden conformal sector, as in some F-theory GUT models. In the Delta-deformed Supersymmetric Standard Model (DSSM), the Higgs fields are operators with non-trivial scaling dimension 1 < Delta < 2. The Kahler metric is singular at the origin of field space due to the presence of quasi-hidden sector states which get their mass from the Higgs vevs. The presence of these extra states leads to the fact that even as Delta approaches 1, the DSSM does not reduce to the MSSM. In particular, the Higgs can naturally be heavier than the W- and Z-bosons. Perturbative gauge coupling unification, a large top quark Yukawa, and consistency with precision electroweak can all be maintained for Delta close to unity. Moreover, such values of Delta can naturally be obtained in string-motivated constructions. The quasi-hidden sector generically contains states charged under SU(5)_GUT as well as gauge singlets, leading to a rich, albeit model-dependent, collider phenomenology.

Semiholographic Quantum Criticality

We identify the near-critical effective theory (EFT) for a wide class of low-temperature phase transitions found via holography. The EFT is of the semiholographic type and describes both holographic Berezinskii-Kosterlitz-Thouless and second-order transitions with nontrivial scaling. It is a simple generalization of the Ginzburg-Landau-Wilson paradigm to systems with an emergent (or hidden) conformal sector. Having identified the near-critical EFT, we explore its basic phenomenology by computing critical exponents and low-frequency correlators.

The conformal sector of F-theory GUTs

D3-brane probes of exceptional Yukawa points in F-theory GUTs are natural hidden sectors for particle phenomenology. We find that coupling the probe to the MSSM yields a new class of N = 1 conformal fixed points with computable infrared R-charges. Quite surprisingly, we find that the MSSM only weakly mixes with the strongly coupled sector in the sense that the MSSM fields pick up small exactly computable anomalous dimensions. Additionally, we find that although the states of the probe sector transform as complete GUT multiplets, their coupling to Standard Model fields leads to a calculable threshold correction to the running of the visible sector gauge couplings which improves precision unification. We also briefly consider scenarios in which SUSY is broken in the hidden sector. This leads to a gauge mediated spectrum for the gauginos and first two superpartner generations, with additional contributions to the third generation superpartners and Higgs sector.

Semi-holographic Fermi liquids

We show that the universal physics of recent holographic non-Fermi liquid models is captured by a semi-holographic description, in which a dynamical boundary field is coupled to a strongly coupled conformal sector having a gravity dual. This allows various generalizations, such as a dynamical exponent and lattice and impurity effects. We examine possible relevant deformations, including multi-trace terms and spin-orbit effects. We discuss the matching onto the UV theory of the earlier work, and an alternate description in which the boundary field is integrated out.

The gauge unparticles (“ungluons”)

A field model for a quark and an antiquark binding is described. Quarks interact via a gauge unparticle ("ungluons"). The model is formulated in terms of Lagrangian which features the source field $S(x)$ which becomes a local pseudo-Goldstone field of conformal symmetry - the pseudodilaton mode and from which the gauge non-primary unparticle field is derived by $B_{\mu}(x) \sim\partial_{\mu} S(x)$. Because the conformal sector is strongly coupled, the mode $S(x)$ may be one of new states accessible at high energies. We have carried out an analysis of the important quantity that enters in the "ungluon" exchange pattern - the "ungluon" propagator.

Desensitizing inflation from the Planck scale

A new mechanism to control Planck-scale corrections to the inflationary eta parameter is proposed. A common approach to the eta problem is to impose a shift symmetry on the inflaton field. However, this symmetry has to remain unbroken by Planck-scale effects, which is a rather strong requirement on possible ultraviolet completions of the theory. In this paper, we show that the breaking of the shift symmetry by Planck-scale corrections can be systematically suppressed if the inflaton field interacts with a conformal sector. The inflaton then receives an anomalous dimension in the conformal field theory, which leads to sequestering of all dangerous high-energy corrections. We analyze a number of models where the mechanism can be seen in action. In our most detailed example we compute the exact anomalous dimensions via a-maximization and show that the eta problem can be solved using only weakly-coupled physics.

Superconformal flavor simplified

A simple explanation of the flavor hierarchies can arise if matter fields interact with a conformal sector and different generations have different anomalous dimensions under the CFT. However, in the original study by Nelson and Strassler many supersymmetric models of this type were considered to be ‘incalculable’ because the R-charges were not sufficiently constrained by the superpotential. We point out that nearly all such models are calculable with the use of a-maximization. Utilizing this, we construct the simplest vector-like flavor models and discuss their viability. A significant constraint on these models comes from requiring that the visible gauge couplings remain perturbative throughout the conformal window needed to generate the hierarchies. However, we find that there is a small class of simple flavor models that can evade this bound.

Unparticle self-interactions

We develop techniques for studying the effects of self-interactions in the conformal sector of an unparticle model. Their physics is encoded in the higher n-point functions of the conformal theory. We study inclusive processes and argue that the inclusive production of unparticle stuff in standard model processes due to the unparticle self-interactions can be decomposed using the conformal partial wave expansion and its generalizations into a sum over contributions from the production of various kinds of unparticle stuff, corresponding to different primary conformal operators. Such processes typically involve the production of unparticle stuff associated with operators other than those to which the standard model couples directly. Thus just as interactions between particles allow scattering processes to produce new particles in the final state, so unparticle self-interactions cause the production of various kinds of unparticle stuff. We discuss both inclusive and exclusive methods for computing these processes. The resulting picture, we believe, is a step towards understanding what unparticle stuff "looks like" because it is quite analogous to way we describe the production and scattering of ordinary particles in quantum field theory, with the primary conformal operators playing the role of particles and the coefficients in the conformal partial wave expansion (and its generalization to include more fields) playing the role of amplitudes. We exemplify our methods in the 2D toy model that we discussed previously in which the Banks-Zaks theory is exactly solvable.

Collider effects of unparticle interactions in multiphoton signals

A new model of physics, with a hidden conformal sector which manifests itself as an unparticle coupling to standard model particles effectively through higher dimensional operators, predicts strong collider signals due to unparticle self-interactions. We perform a complete analysis of the most spectacular of these signals at the hadron collider, $pp(\overline{p})\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\gamma}$ and $\ensuremath{\gamma}\ensuremath{\gamma}gg$. These processes can go through the three-point unparticle self-interactions as well as through some $s$ and $t$ channel diagrams with one and/or two unparticle exchanges. We study the contributions of individual diagrams classified with respect to the number of unparticle exchanges and discuss their effect on the cross sections at the Tevatron and the LHC. We also restrict the Tevatron bound on the unknown coefficient of the three-point unparticle correlator. With the availability of data from the Tevatron, and the advent of the data emerging from the LHC, these interactions can provide a clear and strong indication of unparticle physics and distinguish this model from other beyond the standard model scenarios.

Searching for a dilaton decaying to muon pairs at the LHC

We analyze the decays to muons of a light dilaton produced via vector boson fusion at the LHC. We investigate models in which the electroweak symmetry breaking is triggered by a spontaneously broken, approximately conformal sector. Taking into account the possibility of shifts in the dilaton Yukawa couplings to muons, we find a rather promising scenario for the conformal model search in the channel, with the possibility for a dilaton discovery at a delivered luminosity of $100\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ at the LHC or, alternatively, for an extension of the exclusion zone in the model parameter space, until now fixed by the Tevatron.

Unsterile-active neutrino mixing: Consequences on radiative decay and bounds from the x-ray background

We consider a sterile neutrino to be an unparticle, namely, an unsterile neutrino, with anomalous dimension $\ensuremath{\eta}$ and study its mixing with a canonical active neutrino via a seesaw mass matrix. We show that there is no unitary transformation that diagonalizes the mixed propagator and a field redefinition is required. The propagating or ``mass'' states correspond to an unsterilelike and activelike mode. The unsterile mode features a complex pole or resonance for $0\ensuremath{\le}\ensuremath{\eta}l1/3$ with an ``invisible width'' which is the result of the decay of the unsterile mode into the active mode and the massless particles of the hidden conformal sector. For $\ensuremath{\eta}\ensuremath{\ge}1/3$, the complex pole disappears, merging with the unparticle threshold. The active mode is described by a stable pole, but ``inherits'' a nonvanishing spectral density above the unparticle threshold as a consequence of the mixing. We find that the radiative decay width of the unsterile neutrino into the active neutrino (and a photon) via charged current loops, is suppressed by a factor $\ensuremath{\sim}[2{sin}^{2}({\ensuremath{\theta}}_{0})\frac{{M}^{2}}{{\ensuremath{\Lambda}}^{2}}{]}^{\ensuremath{\eta}/(1\ensuremath{-}\ensuremath{\eta})}$, where ${\ensuremath{\theta}}_{0}$ is the mixing angle for $\ensuremath{\eta}=0$, $M$ is approximately the mass of the unsterile neutrino, and $\ensuremath{\Lambda}\ensuremath{\gg}M$ is the unparticle scale. The suppression of the radiative (visible) decay width of the sterile neutrino weakens the bound on the mass and mixing angle from the x-ray or soft gamma-ray background.

Conformal sector of quantum Einstein gravity in the local potential approximation: Non-Gaussian fixed point and a phase of unbroken diffeomorphism invariance

We explore the nonperturbative renormalization group flow of quantum Einstein gravity (QEG) on an infinite dimensional theory space. We consider ``conformally reduced'' gravity where only fluctuations of the conformal factor are quantized and employ the local potential approximation for its effective average action. The requirement of ``background independence'' in quantum gravity entails a partial differential equation governing the scale dependence of the potential for the conformal factor which differs significantly from that of a scalar matter field. In the infinite dimensional space of potential functions we find a Gaussian as well as a non-Gaussian fixed point which provides further evidence for the viability of the asymptotic safety scenario. The analog of the invariant cubic in the curvature which spoils perturbative renormalizability is seen to be unproblematic for the asymptotic safety of the conformally reduced theory. The scaling fields and dimensions of both fixed points are obtained explicitly and possible implications for the predictivity of the theory are discussed. Spacetime manifolds with ${R}^{d}$ as well as ${S}^{d}$ topology are considered. Solving the flow equation for the potential numerically we obtain examples of renormalization group trajectories inside the ultraviolet critical surface of the non-Gaussian fixed point. The quantum theories based upon some of them show a phase transition from the familiar (low energy) phase of gravity with spontaneously broken diffeomorphism invariance to a new phase of unbroken diffeomorphism invariance; the latter phase is characterized by a vanishing expectation value of the metric.

The nature of the electroweak Higgs sector

In this talk I will first discuss the main features of electroweak symmetry breaking in the Standard Model and in particular I will focus on the Higgs sector responsible thereof. I will highlight the deficiencies of the Standard Model both from the experimental (Dark Matter, baryogenesis,...) and theoretical (ultraviolet sensitivity of the Higgs mass, unexplained flavor textures in the quark and lepton sectors, lack of unification of gauge couplings, strong CP problem,...) points of view which largely motivate extending it to Beyond the Standard Model scenarios. We then briefly review some of the scenarios which aim at solving some of the above problems. In particular we have discussed the minimal supersymmetric extension of the Standard Model, Little Higgs models, gauge-Higgs unification scenarios and the possibility of the Higgs living in a conformal sector (un-Higgs) as a solution to the hierarchy problem. In all cases we have focused on the electroweak sector of the models and the particular solution they offer to the Standard Model problems.

Renormalization group flow off(R)gravity

Understanding gravity as a fundamental theory implies understanding its behavior as we move across different length scales. In the present thesis, we have investigated this scale-dependent behavior by studying the renormalization group flow of gravity. A central focus of our investigations was the asymptotic safety scenario, which posits the existence of a non-trivial fixed point of the gravitational renormalization group controlling the behavior of the theory in the ultraviolet and providing it with a predictive and well-defined high-energy limit. Our main tool was a continuous Wilsonian renormalization group technique, the functional renormalization group equation. Computations within this framework rely on truncation approximations, whereby the full renormalization group flow is projected onto a subspace of the couplings of the theory. The reliability of the results thus obtained is assessed by verifying their stability under the gradual extension of the truncation subspace. The simplest, non-trivial gravity truncation one may consider is the Einstein-Hilbert truncation, in which evidence was first found for a non-trivial fixed point of gravity in support of the asymptotic safety scenario. The crucial question is then whether or not this fixed point persists under further enlargement of the truncation subspaces. In this thesis, we have tackled this question by following three complementary strategies. First, in Chapter 3, we investigated the renormalization group flow of gravity restricted to the conformal sector. This simplification allowed us to consider truncations containing terms which would be otherwise intractable for technical reasons, and thus obtain a rough picture of the effect of those terms on the behavior of the complete theory. A second strategy, which we followed in Chapters 4 and 5, returning to the case of full gravity, was to construct a functional renormalization group equation that allowed us to study general truncations spanned by arbitrary functions $f(R)$ of the curvature scalar, and hence investigate large sectors of the full renormalization group flow space. Lastly, in Chapter 6, we included in our truncation terms which are known to be particularly problematic from the point of view of perturbative quantization. First, we moved beyond the $f(R)$-case by explicitly including four-derivative tensorial operators in our truncation, and then added a minimally coupled, massless scalar field to our truncation. Remarkably, in all of these extensions a non-trivial ultraviolet fixed point was found. The coherent picture that arises from these studies provides significant evidence in favor of the asymptotic safety scenario, and suggests that quantized gravity remains predictive at arbitrarily small scales.