UV Completion Research Articles

Loops, local corrections and warping in the LVS and other type IIB models

To establish metastable de Sitter vacua or even just scale-separated AdS, control over perturbative corrections to the string-derived leading-order 4d lagrangian is crucial. Such corrections can be classified in three types: first, there are genuine loop effects, insensitive to the UV completion of the 10d theory. Second, there are local α′ corrections or, equivalently, 10d higher-dimension operators which may or may not be related to loop-effects. Third, warping corrections affect the 4d Kahler potential but are expected not to violate the 4d no-scale structure. With this classification in mind, we attempt to derive the Berg-Haack-Pajer conjecture for Kahler corrections in type-IIB Calabi-Yau orientifolds and extend it to include further terms. This is crucial since the interesting applications of this conjecture are in the context of generic Calabi-Yau geometries rather than in the torus-based models from which the main motivation originally stems. As an important by-product, we resolve a known apparent inconsistency between the parametric behaviour of string loop results and field-theoretic expectations. Our findings lead to some interesting new statements concerning loop effects associated with blowup-cycles, loop corrections in fibre inflation, and possible logarithmic effects in the Kahler and scalar potential.

Integrating out beyond tree level and relativistic superfluids

We revisit certain subtleties of renormalization that arise when one derives a low-energy effective action by integrating out the heavy fields of a more complete theory. Usually these subtleties are circumvented by matching some physical observables, such as scattering amplitudes, but a more involved procedure is required if one is interested in deriving the effective theory to all orders in the light fields (but still to fixed order in the derivative expansion). As a concrete example, we study the U(1) Goldstone low-energy effective theory that describes the spontaneously broken phase of a ϕ4 theory for a complex scalar. Working to lowest order in the derivative expansion, but to all orders in the Goldstones, we integrate out the radial mode at one loop and express the low-energy effective action in terms of the renormalized couplings of the UV completion. This yields the one-loop equation of state for the superfluid phase of (complex) ϕ4. We perform the same analysis for a renormalizable scalar SO(N) theory at finite chemical potential, integrating out the gapped Goldstones as well, and confirm that the effective theory for the gapless Goldstone exhibits no obvious sign of the original SO(N) symmetry.

Spinning sum rules for the dimension-six SMEFT

We construct new dispersive sum rules for the effective field theory of the standard model at mass dimension six. These spinning sum rules encode information about the spin of UV states: the sign of the IR Wilson coefficients carries a memory of the dominant spin in the UV completion. The sum rules are constructed for operators containing scalars and fermions, although we consider the dimension-six SMEFT exhaustively, outlining why equivalent relations do not hold for the remaining operators. As with any dimension-six dispersive argument, our conclusions are contingent on the absence of potential poles at infinity — so-called boundary terms — and we discuss in detail where these are expected to appear. There are a number of phenomenological applications of spinning sum rules, and as an example we explore the connection to the Peskin-Takeuchi parameters and, more generally, the set of oblique parameters in universal theories.

Unitarization of infinite-range forces: graviton-graviton scattering

A method to unitarize the scattering amplitude produced by infinite-range forces is developed and applied to Born terms. In order to apply S-matrix techniques, based on unitarity and analyticity, we first derive an S-matrix free of infrared divergences. This is achieved by removing a divergent phase factor due to the interactions mediated by the massless particles in the crossed channels, a procedure that is related to previous formalisms to treat infrared divergences. We apply this method in detail by unitarizing the Born terms for graviton-graviton scattering in pure gravity and we find a scalar graviton-graviton resonance with vacuum quantum numbers (JPC = 0++) that we call the graviball. Remarkably, this resonance is located below the Planck mass but deep in the complex s-plane (with s the usual Mandelstam variable), so that its effects along the physical real s axis peak for values significantly lower than this scale. This implies that the corrections to the leading-order amplitude in the gravitational effective field theory are larger than expected from naive dimensional analysis for s around and above the peak position. We argue that the position and width of the graviball are reduced when including extra light fields in the theory. This could lead to phenomenological consequences in scenarios of quantum gravity with a large number of such fields or, in general, with a low-energy ultraviolet completion. We also apply this formalism to two non-relativistic potentials with exact known solutions for the scattering amplitudes: Coulomb scattering and an energy-dependent potential obtained from the Coulomb one with a zero at threshold. This latter case shares the same J = 0 partial-wave projected Born term as the graviton-graviton case, except for a global factor. We find that the relevant resonance structure of these examples is reproduced by our methods, which represents a strong indication of their robustness.

From conformal correlators to analytic S-matrices: CFT1/QFT2

We study families of one-dimensional CFTs relevant for describing gapped QFTs in AdS2. Using the Polyakov bootstrap as our main tool, we explain how S-matrices emerge from the flat space limit of CFT correlators. In this limit we prove that the CFT OPE density matches that of a generalized free field, and that this implies unitarity of the S-matrix. We establish a CFT dispersion formula for the S-matrix, proving its analyticity except for singularities on the real axis which we characterize in terms of the CFT data. In particular positivity of the OPE establishes that any such S-matrix must satisfy extended unitarity conditions. We also carefully prove that for physical kinematics the S-matrix may be more directly described by a phase shift formula. Our results crucially depend on the assumption of a certain gap in the spectrum of operators. We bootstrap perturbative AdS bubble, triangle and box diagrams and find that the presence of anomalous thresholds in S-matrices are precisely signaled by an unbounded OPE arising from violating this assumption. Finally we clarify the relation between unitarity saturating S-matrices and extremal CFTs, establish a mapping between the dual S-matrix and CFT bootstraps, and discuss how our results help understand UV completeness or lack thereof for specific S-matrices.

On the classification of UV completions of integrable Toverline{T} deformations of CFT

It is well understood that 2d conformal field theory (CFT) deformed by an irrelevant Toverline{T} perturbation of dimension 4 has universal properties. In particular, for the most interesting cases, the theory develops a singularity in the ultra-violet (UV), signifying a shortest possible distance, with a Hagedorn transition in applications to string theory. We show that by adding an infinite number of higher [ Toverline{T} ]s>1 irrelevant operators of positive integer scaling dimension 2(s+1) with tuned couplings, this singularity can be resolved and the theory becomes UV complete with a Virasoro central charge cUV> cIR consistent with the c-theorem. We propose an approach to classifying the possible UV completions of a given CFT perturbed by [ Toverline{T} ]s that are integrable. The main tool utilized is the thermodynamic Bethe ansatz. We study this classification for theories with scalar (diagonal) factorizable S-matrices. For the Ising model with cIR = frac{1}{2} we find 3 UV completions based on a single massless Majorana fermion description with cUV = frac{7}{10} and frac{3}{2} , which both have mathcal{N} = 1 SUSY and were previously known, and we argue that these are the only solutions to our classification problem based on this spectrum of particles. We find 3 additional ones with a spectrum of 8 massless particles related to the Lie group E8 appropriate to a magnetic perturbation with cUV = frac{21}{22},frac{15}{12} , and frac{31}{2} . We argue that it is likely there are more cases for this E8 spectrum. We also study simpler cases based on su(3) and su(4) where we can propose complete classifications. For su(3) the infrared (IR) theory is the 3-state Potts model with cIR = frac{4}{5} and we find 3 completions with frac{4}{5} < cUV≤ frac{16}{5} . For the su(4) case, which has 3 particles and cIR = 1, and we find 11 UV completions with 1 < cUV ≤ 5, most of which were previously unknown.

Causality constraints on black holes beyond GR

We derive causality constraints on the simplest scalar-tensor theories in which black holes differ from what General Relativity predicts, a scalar coupled to the Gauss-Bonnet or the Chern-Simons terms. Demanding that time advances are unobservable within the regime of validity of these effective field theories, we find their cutoff must be parametrically of the same size as the inverse Schwarzschild radius of the black holes for which the non-standard effects are of order one. For astrophysical black holes within the range of current gravitational wave detectors, this means a cutoff length of the order of kilometers. We further explore the leading additional higher-dimensional operators potentially associated with the scale of UV completion and discuss their phenomenological implications for gravitational wave science.

Well-posed UV completion for simulating scalar Galileons

The Galileon scalar field theory is a prototypical example of an effective field theory that exhibits the Vainshtein screening mechanism, which is incorporated into many extensions to Einstein gravity. The Galileon describes the helicity zero mode of gravitational radiation, the presence of which has significant implications for predictions of gravitational waves from orbiting objects, and for tests of gravity sensitive to additional polarizations. Because of the derivative nature of their interactions, Galileons are superficially not well-posed as effective field theories. Although this property is properly understood merely as an artifact of the effective field theory truncation, and is not theoretically worrisome, at the practical level it nevertheless renders numerical simulation highly problematic. Notwithstanding, previous numerical approaches have successfully evolved the system for reasonable initial data by slowly turning on the interactions. We present here two alternative approaches to improving numerical stability in Galileon numerical simulations. One of these is a minor modification of previous approaches, which introduces a low pass filter that amounts to imposing a UV cutoff together with a relaxation method of turning on interactions. The second approach amounts to constructing a (numerical) UV completion for which the dynamics of the high momentum modes is under control, and for which it is unnecessary to slowly turn on nonlinear interactions. We show that numerical simulations of the UV theory successfully reproduce the correct Galileon dynamics at low energies, consistent with the low-pass filter method and with previous numerical simulations.

Sterile neutrino portals to Majorana dark matter: effective operators and UV completions

Stringent constraints on the interactions of dark matter with the Standard Model suggest that dark matter does not take part in gauge interactions. In this regard, the possibility of communicating between the visible and dark sectors via gauge singlets seems rather natural. We consider a framework where the dark matter talks to the Standard Model through its coupling to sterile neutrinos, which generate active neutrino masses. We focus on the case of Majorana dark matter, with its relic abundance set by thermal freeze-out through annihilations into sterile neutrinos. We use an effective field theory approach to study the possible sterile neutrino portals to dark matter. We find that both lepton-number-conserving and lepton-number-violating operators are possible, yielding an interesting connection with the Dirac/Majorana character of active neutrinos. In a second step, we open the different operators and outline the possible renormalisable models. We analyse the phenomenology of the most promising ones, including a particular case in which the Majorana mass of the sterile neutrinos is generated radiatively.

Non-topological logarithmic corrections in minimal gauged supergravity

We compute the logarithmic correction to the entropy of asymptotically AdS4 black holes in minimal mathcal{N} = 2 gauged supergravity. We show that for extremal black holes the logarithmic correction computed in the near horizon geometry agrees with the result in the full geometry up to zero mode contributions, thus clarifying where the quantum degrees of freedom lie in AdS spacetimes. In contrast to flat space, we observe that the logarithmic correction for supersymmetric black holes can be non-topological in AdS as it is controlled by additional four-derivative terms other than the Euler density. The available microscopic data and results in 11d supergravity indicate that the full logarithmic correction is topological, which suggests that the topological nature of logarithmic corrections could serve as a diagnosis of whether a low-energy gravity theory admits an ultraviolet completion.

NLO QCD renormalization group evolution for nonleptonic ΔF=2 transitions in the SMEFT

We present for the first time Next-to-Leading (NLO) QCD renormalization group (RG) evolution matrices for nonleptonic $\mathrm{\ensuremath{\Delta}}F=2$ transitions in the Standard Model effective field theory (SMEFT). To this end we transform first the known two-loop QCD anomalous dimension matrices (ADMs) of the BSM (Beyond the SM) operators in the so-called Buras Misiak Urban basis into the ones in the common weak effective theory (WET) basis (the so-called Jenkins Manohar Stoffer basis) for which tree-level and one-loop matching to the SMEFT are already known. This subsequently allows us to find the two-loop QCD ADMs for the SMEFT nonleptonic $\mathrm{\ensuremath{\Delta}}F=2$ operators in the Warsaw basis. Having all these ingredients we investigate the impact of these NLO QCD effects on the QCD RG evolution of SMEFT Wilson coefficients for nonleptonic $\mathrm{\ensuremath{\Delta}}F=2$ transitions from the new physics scale $\mathrm{\ensuremath{\Lambda}}$ down to the electroweak scale ${\ensuremath{\mu}}_{\mathrm{ew}}$. The main benefit of these new contributions is that they allow one to remove renormalization scheme dependences present in the one-loop matchings both between the WET and SMEFT and also between SMEFT and a chosen UV completion. But the Next-to-Leading (NLO) QCD effects, calculated here in the Naive dimensional regularisation minimal subtraction scheme, turn out to be small, in the ballpark of a few percent but larger than one-loop Yukawa top effects when only the $\mathrm{\ensuremath{\Delta}}F=2$ operators are considered. The more complicated class of nonleptonic $\mathrm{\ensuremath{\Delta}}F=1$ decays will be presented soon in another publication.

Phenomenological analysis of multi-pseudoscalar mediated dark matter models

Non-minimal simplified extensions of the Standard Model have gained considerable currency in the context of dark matter searches at the LHC, since they predict enhanced mono-Higgs and mono-W/Z signatures over large parts of the parameter space. However, these non-minimal models obviously lack the simplicity and directness of the original simplified models, and are more heavily dependent on the model assumptions. We propose to classify these models generically on the basis of additional mediator(s) and dark matter particles. As an example, we take up a scenario involving multiple pseudoscalar mediators, and a single Dirac dark matter particle, the latter being a popular introduction to ensure ultraviolet completion of theories with multiple pseudoscalar fields. In the chosen scenario, we discuss the viable channels and signatures of relevance at the future runs of the LHC. These are then compared with the minimal simplified scenarios and distinguishing features are pinpointed.

Light vectors coupled to anomalous currents with harmless Wess-Zumino terms

We reconsider the case of light vectors coupled to anomalous fermionic currents, focusing on the interplay between ultraviolet and infrared dynamics. Taking as a general framework the gauging of the Standard Model accidental symmetries, we show that it is possible to devise an anomaly-free ultraviolet completion with mostly chiral heavy fermions such that anomalous Wess-Zumino terms are suppressed in the infrared, thus relaxing would-be strong bounds from the longitudinal emission of light vectors coupled to nonconserved currents. We classify such scenarios and show that they will be extensively probed at the high-luminosity phase of the LHC via the measurement of the $h\ensuremath{\rightarrow}Z\ensuremath{\gamma}$ rate and the direct search for nondecoupling charged leptons.

Superconformal index for [formula omitted][formula omitted] Chern-Simons quiver gauge theories

We compute superconformal indices for N=3ADEˆ Chern-Simons quiver gauge theories with a product gauge group ∏iU(N)i, using the method of supersymmetric localization. We also perform a large N analysis of the index. This index includes contribution from non zero magnetic flux sector. The fact that these theories have a weakly coupled UV completion in terms of N=3 supersymmetric Chern-Simons Yang-Mills theories enables us to apply the localization technique. Such theories have dual M-theory description on AdS4×M7, where M7 is a tri-Sasaki Einstein manifold.

Four-fermion operators at dimension 6: Dispersion relations and UV completions

A major task in phenomenology today is constraining the parameter space of Standard Model effective field theory and constructing models of fundamental physics from which the Standard Model derives. To this effect, we report an exhaustive list of sum rules for 4-fermion operators of dimension 6, connecting low-energy Wilson coefficients to cross sections in the UV. Unlike their dimension-8 counterparts which are amenable to a positivity bound, the discussion here is more involved due to the weaker convergence and indefinite signs of the dispersion integrals. We illustrate this by providing examples with weakly coupled UV completions leading to opposite signs of the Wilson coefficients for both convergent and nonconvergent dispersion integrals. We further decompose dispersion integrals under weak isospin and color groups, which lead to a tighter relation between IR measurements and UV models. These sum rules can become an effective tool for constructing consistent UV completions for Standard Model effective field theory following the prospective measurement of these Wilson coefficients.

Misanthropic entropy and renormalization as a communication channel

A central physical question is the extent to which infrared (IR) observations are sufficient to reconstruct a candidate ultraviolet (UV) completion. We recast this question as a problem of communication, with messages encoded in field configurations of the UV being transmitted to the IR degrees of freedom via a noisy channel specified by renormalization group (RG) flow, with noise generated by coarse graining/decimation. We present an explicit formulation of these considerations in terms of lattice field theory, where we show that the “misanthropic entropy” — the mutual information obtained from decimating neighbors — encodes the extent to which information is lost in marginalizing over/tracing out UV degrees of freedom. Our considerations apply both to statistical field theories as well as density matrix renormalization of quantum systems, where in the quantum case, the statistical field theory analysis amounts to a leading-order approximation. As a concrete example, we focus on the case of the 2D Ising model, where we show that the misanthropic entropy detects the onset of the phase transition at the Ising model critical point.

Rigorous bounds on light-by-light scattering

We bound EFT coefficients appearing in 2 → 2 photon scattering amplitudes in four dimensions. After reviewing unitarity and positivity conditions in this context, we use dispersion relations and crossing symmetry to compute sum rules and null constraints. This allows us to derive new rigorous bounds on operators with four, six, and eight derivatives, including two-sided bounds on their ratios. Comparing with a number of partial UV completions, we find that some of our bounds are saturated by the amplitudes that arise from integrating out a massive scalar or axion, while others suggest the existence of unknown amplitudes.

Fermion mass hierarchy and lepton flavor violation using CP symmetry

In this paper, we present a model which employs [Formula: see text] symmetries where quark mixing and charged leptons masses are explained by following some texture. To achieve neutrino mass and mixing, we write a nonrenormalizable Lagrangian using type II seesaw mechanism by assuming [Formula: see text] couplings predicting no CP violation. Then, we calculate the value of the couplings for both normal and inverted ordering of neutrino masses. We propose a mechanism of ultraviolet (UV) completion that motivates the higher-dimensional Lagrangian in the neutrino sector. We also calculate the branching fraction of lepton flavor violating decays driven by triplet scalar for the model. Later, it is shown that the model can also accommodate maximal CP violation by breaking the CP symmetry spontaneously.

Holographic models of composite Higgs in the Veneziano limit. Part II. Fermionic sector

We continue our study of strongly-coupled, approximately scale-invariant gauge theories with a large number of flavours, which provide a suitable ultraviolet completion of the composite-Higgs scenario. We identify the requisite operators to realise partial compositeness of the Standard-Model fermions. In order to compute the spectrum of composite fermionic states, we extend the bottom-up holographic models, which we previously introduced to capture the main features of the non-perturbative dynamics in the Veneziano limit, by adding fermion fields in the bulk. We identify regions in parameter space where some fermionic bound states become light, depending in particular on the number of flavours, the operator scaling dimensions, and the bulk Yukawa couplings. We also observe a dense spectrum of states, when multi-scale dynamics is induced by a large backreaction of bulk scalars on the geometry. Adapting the formalism of the holographic Wilsonian renormalisation group, we study the linear coupling between the composite and elementary fermions, as a function of energy scale. We find that, in some circumstances, the associated operators are dangerously irrelevant: the renormalisation-group flow gives rise to a large linear coupling in the infrared, even when it is irrelevant from the point of view of the ultraviolet fixed point. We finally compute the partially composite spectrum, correlate it with the analysis of the flow, and assess the potential phenomenological implications, e.g. for the top-quark partners.

2-2-holes simplified

Quadratic gravity illustrates how a replacement for black holes can emerge from a UV completion of gravity. 2-2-holes are extremely compact horizonless objects with an entropy S22 due to trapped normal matter, and in this way they are conceptually easy to understand. But the field equations are cumbersome and the numerical analysis has so far been restricted to relatively small size solutions. Here we show how the properties of arbitrarily large 2-2-holes can be found, including the time delay for gravitational wave echoes and the result T∞S22=M/2. The starting point is to formulate the metric in terms of the tortoise coordinate, and to have one of the two metric functions be a conformal factor. A large conformally-related volume becomes associated with the interior of a 2-2-hole. We also discuss implications for the weak gravity conjecture.