Anomalous Dimension Research Articles

Anomalous dimension and quasinormal modes of flavor branes

We study scalar quasinormal modes in a D3/D7 system holographically dual to a quantum field theory with chiral symmetry breaking at finite temperature. From the bottom-up approach, we consider a nontrivial dilaton profile which is responsible for the anomalous dimension of the quark condensate. It depends on a new parameter q in the model. By varying this parameter, we study the behavior of the massive and massless scalar quasinormal modes. The numerical method that we use is the spectral method, and we find that there is no pure imaginary mode for the massless case but it appears by increasing the parameter q. It is known that this mode becomes tachyonic for massive cases. Then we turn on a pseudoscalar field and using a simple ansatz study its effect on the quasinormal modes of the scalar field. By varying the parameter of the nontrivial dilaton profile in the model, we qualitatively study quasinormal modes in walking theories.

Two-loop anomalous dimensions for small-R jet versus hadronic fragmentation functions

We study the collinear fragmentation of highly energetic jets defined with a small jet radius. In particular, we investigate how the corresponding fragmentation functions differ from their hadronic counterpart defined in the common MS¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{\ extrm{MS}} $$\\end{document} scheme. We find that the anomalous dimensions governing the perturbative evolution of the two fragmentation functions differ starting at the two loop order. We compute for the first time the new anomalous dimensions at two loops and confirm our predictions by comparing the inclusive small-R jet spectrum against a fixed order perturbative calculation at O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(αs2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\alpha}_s^2 $$\\end{document}). To investigate the dependence of the anomalous dimension on the kinematic cutoff variable, we study the fragmentation functions of Cambridge jets defined with a transverse momentum cutoff as opposed to an angular cutoff R. We further study the evolution of the small-R fragmentation function with an alternative cutoff scale, proportional to zR, representing the maximum possible transverse momentum of emissions within a jet. In these cases we find that the two-loop anomalous dimensions coincide with the MS¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{\ extrm{MS}} $$\\end{document} DGLAP ones, highlighting a correspondence between the MS¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{\ extrm{MS}} $$\\end{document} scheme and a transverse-momentum cutoff.

Functional renormalization group approach to dipolar fixed point which is scale invariant but nonconformal

A dipolar fixed point introduced by Aharony and Fisher is a physical example of interacting scale-invariant but nonconformal field theories. We find that the perturbative critical exponents computed in ε expansions violate the conformal bootstrap bound. We formulate the functional renormalization group equations Wetterich and Polchinski to study the fixed point. We present some results in three dimensions within (uncontrolled) local potential approximations (with or without perturbative anomalous dimensions). Published by the American Physical Society 2024

Holography for Sp(2Nc) gauge dynamics: from composite Higgs to technicolour

We study Sp(2Nc) gauge dynamics with two Dirac fermion flavours in the fundamental representation. These strongly coupled systems underlie some composite Higgs models with a global symmetry breaking pattern SU(4)→Sp(4), leading to a light quartet of pseudo-Goldstone bosons that can play the role of the Higgs. Including four-fermion interactions can rotate the vacuum to a technicolour breaking pattern. Using gauge/gravity duality, we study the underlying gauge dynamics. Our model incorporates the Nc-specific running of the fermion anomalous dimension and can thus distinguish between specific gauge groups. We determine the bound-state spectrum of the UV SU(4)→Sp(4) symmetry breaking model, also including fermion masses and mass splitting, and display the Nc dependence. The inclusion of a four-fermion interaction shows the emergence of three Goldstone bosons on the path to technicolour dynamics.

Functional renormalization group for “p = 2” like glassy matrices in the planar approximation II. Ward identities method in the deep IR

This paper, as a continuation of our previous investigation [Nucl. Phys. B 1005 (2024) 116582] aims to study the glassy random matrices with quenched Wigner disorder. In this previous work, we have constructed a renormalization group based on the effective deterministic kinetic spectrum emerging from large N limit, and we extended approximate solutions using standard vertex expansion, at the leading order of the derivative expansion. Now in the following work, by introducing the non-trivial Ward identities which come from the (U(N))×2 symmetry broken of the effective kinetic action, we provide in the deep IR the explicit solution of the functional renormalization group for a model with quartic coupling by solving the Hierarchy to all orders in the local sector, which in particular imply the vanishing of the anomalous dimension. The numerical investigations confirm the first-order phase transition discovered in the vertex expansion framework, both in the active and passive schemes. Finally, we extend the discussion to hermitian matrices.

Field Theory of the Fermi Function.

The Fermi function F(Z,E) accounts for QED corrections to beta decays that are enhanced at either small electron velocity β or large nuclear charge Z. For precision applications, the Fermi function must be combined with other radiative corrections and with scale- and scheme-dependent hadronic matrix elements. We formulate the Fermi function as a field theory object and present a new factorization formula for QED radiative corrections to beta decays. We provide new results for the anomalous dimension of the corresponding effective operator complete through three loops, and resum perturbative logarithms and π enhancements with renormalization-group methods. Our results are important for tests of fundamental physics with precision beta decay and related processes.

Extremal Higgs couplings

We critically assess to what extent it makes sense to bound the Wilson coefficients of dimension-six operators. In the context of Higgs physics, we establish that a closely related observable, cH, is well defined and satisfies a two-sided bound. cH is derived from the low momentum expansion of the scattering amplitude, or the derivative of the amplitude at the origin with respect to the Mandelstam variable s, expressed as M(HiHi→HjHj)=cHs+O(gSM,s−2) where gSM represents all Standard Model couplings. This observable is and, as a result, not sign-definite. We also determine the conditions under which the bound on cH is equivalent to a bound on the dimension-six operator OH=∂|H|2∂|H|2. Published by the American Physical Society 2024

Multiparton Cwebs at five loops

Scattering amplitudes involving multiple partons are plagued with infrared singularities. The soft singularities of the amplitude are captured by the soft function which is defined as the vacuum expectation value of Wilson line correlators. Renormalization properties of soft function allows us to write it as an exponential of the finite soft anomalous dimension. An efficient way to study the soft function is through a set of Feynman diagrams known as Cwebs (webs). We present the mixing matrices and exponentiated colour factors (ECFs) for the Cwebs at five loops that connect six Wilson lines, except those that are related by relabeling of Wilson lines. Further, we express these ECFs in terms of 29 basis colour factors. We also find that this basis can be categorized into two colour structures. Our results are the first key ingredients for the calculation of the soft anomalous dimension at five loops.

Renormalization of beta decay at three loops and beyond

The anomalous dimension for heavy-heavy-light effective theory operators describing nuclear beta decay is computed through three-loop order in the static limit. The result at order Z2α3 corrects a previous result in the literature. An all-orders symmetry is shown to relate the anomalous dimensions at leading and subleading powers of Z at a given order of α. The first unknown coefficient for the anomalous dimension now appears at O(Z2α4). Published by the American Physical Society 2024

Small instanton-induced flavor invariants and the axion potential

Small instantons which increase the axion mass due to an appropriate modification of QCD at a UV scale ΛSI, can also enhance the effect of CP-violating operators to shift the axion potential minimum by an amount, θind, proportional to the flavorful couplings in the SMEFT. Since physical observables must be flavor basis independent, we construct a basis of determinant-like flavor invariants that arise from instanton calculations containing the effects of dimension-six CP-odd operators at the scale . This new basis provides a more reliable estimate of the shift θind, that is severely constrained by neutron electric dipole moment experiments. In particular, for the case of four-quark, semi-leptonic and gluon dipole operators, these invariants are then used to provide improved limits on the ratio of scales for different flavor scenarios. The CP-odd flavor invariants also provide a classification of the leading effects from Wilson coefficients, and as an example, we show that a semi-leptonic four-fermion operator is subdominant compared to the four-quark operators. More generally, the flavor invariants, together with an instanton NDA, can be used to more accurately estimate small instanton effects in the axion potential that arise from any SMEFT operator.

Scaling results for charged sectors of near conformal QCD

We provide the leading near conformal corrections on a cylinder to the scaling dimension of the lowest-lying fixed isospin charge Q operators defined at the lower boundary of the quantum chromodynamics conformal window, Δ˜Q=Δ˜Q*+(mσ4πν)2QΔ3B1+(mπ(θ)4πν)4Q23(1−γ)B2+O(mσ4,mπ8,mσ2mπ4). Here, Δ˜Q/r is the classical ground state energy of the theory on R×Sr3 at fixed isospin charge while Δ˜Q* is the scaling dimension at the leading order in the large charge expansion. In the conformal limit mσ=mπ=0, the state-operator correspondence implies Δ˜Q=Δ˜Q*. The near-conformal corrections are expressed in powers of the dilaton and pion masses in units of the chiral symmetry breaking scale 4πν with the θ-angle dependence encoded directly in the pion mass. The characteristic Q-scaling is dictated by the quark mass operator anomalous dimension γ and the one characterizing the dilaton potential Δ. The coefficients Bi with i=1,2 depend on the geometry of the cylinder and properties of the nearby conformal field theory. Published by the American Physical Society 2024

Hybrid spectroscopy within the graviton soft-wall model

In this analysis, the so-called holographic graviton soft-wall (GSW) model, first developed to investigate the glueball spectrum, has been adopted to predict the masses of hybrids with different quantum numbers. Results have been compared with other models and lattice calculations. We have extended the GSW model by introducing two modifications based on anomalous dimensions in order to improve our agreement with other calculations and to remove the initial degeneracy not accounted for by lattice predictions. These modifications do not involve new parameters. The next step has been to identify which of our calculated states agree with the PDG data, leading to experimental hybrids. The procedure has been extended to include hybrids made of heavy quarks by incorporating the quark masses into the model. Published by the American Physical Society 2024

Interpolating bremsstrahlung function in ABJM model

In ABJM theory, enriched RG flows between circular 1/6 BPS bosonic and 1/2 BPS fermionic Wilson loops have been introduced in L. Castiglioni [L. Castiglioni, S. Penati, M. Tenser, and D. Trancanelli, Interpolating Wilson loops and enriched RG flows, .]. These flows are triggered by deformations corresponding to parametric 1/6 BPS fermionic loops. In this paper, we revisit the study of these operators, but instead of circular contours, we consider an interpolating cusped line and a latitude and study their RG flow in perturbation theory. This allows for the definition of a bremsstrahlung function away from fixed points. We generalize to this case the known cusp/latitude correspondence that relates the bremsstrahlung function to a latitude Wilson loop. We find that away from the conformal fixed points the ordinary identity is broken by the conformal anomaly in a controlled way. From a defect perspective, the breaking of the correspondence can be traced back to the appearance of an anomalous dimension for fermionic operators localized on the defect. As a by-product, we provide a brand new result for the two-loop cusp anomalous dimension of the 1/6 BPS fermionic and the 1/6 BPS bosonic Wilson lines. Published by the American Physical Society 2024

QCD effects in electroweak WZjj\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$WZjj$$\\end{document} production at current and future hadron colliders

We present an update of an existing implementation of WZjj production via vector-boson scattering in the framework of the POWHEG BOX program. In particular, previously unavailable semi-leptonic and fully hadronic decay modes of the intermediate vector bosons are provided, and operators of dimension six in an effective-field theory approach to account for physics beyond the Standard Model in the electroweak sector are included. For selected applications phenomenological results are provided to illustrate the capabilities of the new program. The impact of the considered dimension-six operators on experimentally accessible distributions is found to be small for current LHC energies, but enhanced in the kinematic reach of a potential future hadron collider with an energy of 100 TeV. The relevance of fully accounting for spin correlations and off-shell effects in the decay system is explored by a comparison with results obtained with the MadSpin tool that are based on an approximate treatment of the leptonic final state resulting from vector boson scattering processes. For selected semi-leptonic and hadronic decay modes we demonstrate the sensitivity of realistic signal selection procedures on QCD corrections and parton-shower effects.

Beyond the tensionless limit: integrability in the symmetric orbifold

The symmetric orbifold of \U0001d54b4 is exactly dual to string theory on AdS3 × S3 × \U0001d54b4 with minimal (k = 1) NS-NS flux. In this paper we study the perturbation of the symmetric orbifold that is dual to switching on R-R flux, and hence to deforming the theory away from the tensionless point. More specifically, we determine systematically the action of a centrally extended supersymmetry algebra on the CFT states, and deduce from it the anomalous conformal dimensions. In the w-twisted sector with large w the structure is similar to what was found for N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 SYM: the basic excitations are multi-magnons whose individual dispersion relation is fixed by symmetry, and the comparison with the BMN answer suggests that the result is true to all orders in perturbation theory. Finally we show that the multi-magnon states interact via an integrable S-matrix and possess a natural family of bound states.

Holography of broken U(1) symmetry

We examine the Abelian Higgs model in (d + 1)-dimensional anti-de Sitter space with an ultraviolet brane. The gauge symmetry is broken by a bulk Higgs vacuum expectation value triggered on the brane. We propose two separate Goldstone boson equivalence theorems for the boundary and bulk degrees of freedom. We compute the holographic self-energy of the gauge field and show that its spectrum is either a continuum, gapped continuum, or a discretuum as a function of the Higgs bulk mass. When the Higgs has no bulk mass, the AdS isometries are unbroken. We find in that case that the dual CFT has a non-conserved U(1) current whose anomalous dimension is proportional to the square of the Higgs vacuum expectation value. When the Higgs background weakly breaks the AdS isometries, we present an adapted WKB method to solve the gauge field equations. We show that the U(1) current dimension runs logarithmically with the energy scale in accordance with a nearly-marginal U(1)-breaking deformation of the CFT.

A collinear perspective on the Regge limit

The high energy (Regge) limit provides a playground for understanding all loop structures of scattering amplitudes, and plays an important role in the description of many phenomenologically relevant cross-sections. While well understood in the planar limit, the structure of non-planar corrections introduces many fascinating complexities, for which a general organizing principle is still lacking. We study the structure of multi-reggeon exchanges in the context of the effective field theory for forward scattering, and derive their factorization into collinear operators (impact factors) and soft operators. We derive the structure of the renormalization group consistency equations in the effective theory, showing how the anomalous dimensions of the soft operators are related to those of the collinear operators, allowing us to derive renormalization group equations in the Regge limit purely from a collinear perspective. The rigidity of the consistency equations provides considerable insight into the all orders organization of Regge amplitudes in the effective theory, as well as its relation to other approaches. Along the way we derive a number of technical results that improve the understanding of the effective theory. We illustrate this collinear perspective by re-deriving all the standard BFKL equations for two-Glauber exchange from purely collinear calculations, and we show that this perspective provides a number of conceptual and computational advantages as compared to the standard view from soft or Glauber physics. We anticipate that this formulation in terms of collinear operators will enable a better understanding of the relation between BFKL and DGLAP in gauge theories, and facilitate the analysis of renormalization group evolution equations describing Reggeization beyond next-to-leading order.

Assisted baryon number violation in 4k+2 dimensions

Proton decay in six-dimensions orbifolded on square T2/Z2 is highly suppressed at tree level. This is because baryon number violating (BNV) operators containing only the zero mode of bulk fermions must satisfy the selection rule 32ΔB±12ΔL=0 mod 4. In this article, we show that the above relation does not prohibit mass dimension-six BNV operators containing Kaluza-Klein partners of the bulk fermions. Together with a “spinless” adjoint scalar partner of hypercharge gauge boson (the dark matter candidate), these novel operators generate dark matter assisted proton decay at mass dimension eight. Here, with explicit examples of scalar and vector baryon number violating interactions, we discuss the importance of such ΔB=1=ΔL and ΔB=2=ΔL operators and derive the limit on new physics. Published by the American Physical Society 2024

Gradient Flow Exact Renormalization Group for Scalar Quantum Electrodynamics

Gradient Flow Exact Renormalization Group (GF-ERG) is a framework to define the renormalization group flow of Wilsonian effective action utilizing coarse-graining along the diffusion equations. We apply it for Scalar Quantum Electrodynamics and derive flow equations for the Wilsonian effective action with the perturbative expansion in the gauge coupling. We focus on the quantum corrections to the correlation functions up to the second order of the gauge coupling and discuss the gauge invariance of the GF-ERG flow. We demonstrate that the anomalous dimension of the gauge field agrees with the standard perturbative computation and that the mass of the photon keeps vanishing in general spacetime dimensions. The latter is a noteworthy fact that contrasts with the conventional Exact Renormalization Group formalism in which an artificial photon mass proportional to a cutoff scale is induced. Our results imply that the GF-ERG can give a gauge-invariant renormalization group flow in a non-perturbative way.

Strange metal to insulator transitions in the lowest Landau level

We study the microscopic model of electrons in the partially-filled lowest Landau level interacting via the Coulomb potential by the diagrammatic theory within the GW approximation. In a wide range of filling fractions and temperatures, we find a homogeneous non-Fermi liquid (nFL) state similar to that found in the Sachdev-Ye-Kitaev (SYK) model, with logarithmic corrections to the anomalous dimension. In addition, the phase diagram is qualitatively similar to that of SYK: a first-order transition terminating at a critical end-point separates the nFL phase from a band insulator that corresponds to the fully filled Landau level. This critical point, as well as that of the SYK model—whose critical exponents we determine more precisely—are shown to both belong to the Van der Waals universality class. The possibility of a charge density wave (CDW) instability is also investigated, and we find the homogeneous nFL state to extend down to the ground state for fillings 0.2≲ν≲0.8, while a CDW appears outside this range of fillings at sufficiently low temperatures. Our results suggest that the SYK-like nFL state should be a generic feature of the partially filled lowest Landau level at intermediate temperatures. Published by the American Physical Society 2024