Four-dimensional Theory Research Articles

Whittaker vectors for W\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {W}$$\\end{document}-algebras from topological recursion

We identify Whittaker vectors for Wk(g)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {W}^{\ extsf{k}}(\\mathfrak {g})$$\\end{document}-modules with partition functions of higher Airy structures. This implies that Gaiotto vectors, describing the fundamental class in the equivariant cohomology of a suitable compactification of the moduli space of G-bundles over P2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {P}^2$$\\end{document} for G a complex simple Lie group, can be computed by a non-commutative version of the Chekhov–Eynard–Orantin topological recursion. We formulate the connection to higher Airy structures for Gaiotto vectors of type A, B, C, and D, and explicitly construct the topological recursion for type A (at arbitrary level) and type B (at self-dual level). On the physics side, it means that the Nekrasov partition function for pure N=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {N} = 2$$\\end{document} four-dimensional supersymmetric gauge theories can be accessed by topological recursion methods.

Holomorphic surface defects in four-dimensional Chern-Simons theory

Holomorphic surface defects in four-dimensional Chern-Simons theory

Understanding Non-Invertible Symmetries in Higher Dimensions Using Topological Defects

By constructing Kramers-Wannier-Wegner duality and Z2 duality defects and deriving their crossing relations, this study presents the first examples of codimension one non-invertible symmetries in four-dimensional quantum field theories.

Higher group Weyl symmetry

We study a higher group analog of the Weyl symmetry in four-dimensional quantum field theories. A typical example is that the modified transformation of the 2-form background gauge field replaces the operator-valued Weyl anomaly associated with gauging the 0-form global symmetry. It is analogous to the 2-group global symmetry where the modified transformation of the 2-form background gauge field replaces the operator-valued chiral anomaly associated with gauging the 0-form symmetry. The physical origin of the higher group Weyl symmetry is that under the renormalization group flow, the conserved current mixes with the electromagnetic current that couples with the dynamical gauge field. We can express these effects in the local renormalization group equations in a unified manner.

Model building by coset space dimensional reduction scheme using eight-dimensional coset spaces

We investigate the twelve-dimensional gauge-Higgs unification models with an eight- dimensional coset space as the extra space. For each model, we apply the coset space dimensional reduction procedure and examine the particle contents of the resulting four-dimensional theory. All combinations of inputs to the procedure are exhaustively analyzed under several assumptions. As a result, some twelve-dimensional SO(18) gauge theories lead to models of the SO(10) × U(1) grand unified theory in four dimensions, where fermions of the Standard Model appear in multiple generations along with scalars that may break the electroweak symmetry. The representations of the obtained scalars and fermions are summarized.

Ground state wavefunctions of elliptic relativistic integrable Hamiltonians

We derive ground state eigenfunctions and eigenvalues of various relativistic elliptic integrable models. The models we discuss appear in computations of superconformal indices of four-dimensional theories obtained by compactifying six-dimensional models on Riemann surfaces. These include, among others, the Ruijsenaars-Schneider model and the van Diejen model. The derivation of the eigenfunctions builds on physical inputs, such as conjectured Lagrangian across dimensions IR dualities and assumptions about the behavior of the indices in the limit of compactifications on surfaces with large genus/number of punctures/flux.

The cosmological constant is probably still zero

We consider a wide class of four-dimensional effective field theories in which gravity is coupled to multiple four-forms and their dual scalar fields, with membrane sources charged under the corresponding three-form potentials. Four-form flux, quantised in units of the membrane charges, generically generates a landscape of vacua with a range of values for the cosmological constant that is scanned through membrane nucleation. We list various ways in which the landscape can be made sufficiently dense to be compatible with observations of the current vacuum without running into the empty universe problem. Further, we establish the general criteria required to ensure the absolute stability of the Minkowski vacuum under membrane nucleation and the longevity of those vacua that are parametrically close by. This selects the current vacuum on probabilistic grounds and can even be applied in the classic model of Bousso and Polchinski, albeit with some mild violation of the membrane weak gravity conjecture. We present other models where the membrane weak gravity conjecture is not violated but where the same probabilistic methods can be used to tackle the cosmological constant problem.

Non-local tails in radiation in odd dimensions

Huygens principle violation in a spacetime of odd dimensions leads to the fact that the retarded massless fields of localised sources depend on their history of motion preceding the retarded time. This non-local character of retarded fields should result into the formation of tail signals in the radiation of localised sources. In particular, in gravity theories with odd number of extra spacetime dimensions the gravitational radiation of binary systems should contain the tail terms. In this work, we demonstrate the presence of tail signal in radiation within a simple model of scalar field interacting with the point charge moving on elliptical orbit in three dimensions. We find that the tail term results into the characteristic dependence of radiation power of the charge on time. In particular, its extremum points do not correspond to the moments when the charge passes the pericenter and apocenter of the orbit, in contrast with the four-dimensional theory. We obtain the formulae for the shifts of radiation power extremum points up to the contributions quadratic in the orbital eccentricity. We also compute the spectral distribution of radiation power of the charge. We find that in three dimensions the charge on elliptical orbit radiates into the lower harmonics of the spectrum, compared to the four-dimensional theory. We conjecture that in higher dimensions the character of spectral distributions is opposite — the charge mainly radiates into the higher harmonics of the spectrum.

Effective gravitational couplings of Kaluza-Klein gauge theories

We study the effective gravitational couplings of four-dimensional gauge theories with eight supercharges. The class of theories we analyse are arrived at via Kaluza-Klein compactification of five-dimensional gauge theories. We consider both pure SU(N) Yang-Mills theories with Chern-Simons couplings and the conformal gauge theories with 2N fundamental flavours. The resolvent of the gauge theory plays a crucial role in the calculation of these gravitational couplings. The results obtained from the Seiberg-Witten geometry are matched against independent computations using localisation.

Cosmological phase transitions in composite Higgs models

We investigate cosmological phase transitions in various composite Higgs models consisting of four-dimensional asymptotically-free gauge field theories. Each model may lead to a confinement-deconfinement transition and a phase transition associated with the spontaneous breaking of a global symmetry that realizes the Standard Model Higgs field as a pseudo-Nambu-Goldstone boson. Based on the argument of universality, we discuss the order of the phase transition associated with the global symmetry breaking by studying the renormalization group flow of the corresponding linear sigma model at finite temperature, which is calculated by utilizing the ϵ-expansion technique at the one-loop order. Our analysis indicates that some composite Higgs models accommodate phenomenologically interesting first-order phase transitions. We also explore the confinement-deconfinement transition in a UV-completed composite Higgs model based on a Sp(2Nc) gauge theory. It is found that the first-order phase transition is favored when the number of degrees of freedom for the Sp(2Nc) gauge field is much larger than that of matter fields in the fundamental representation of Sp(2Nc). We comment on the gravitational wave signal generated by the confinement-deconfinement transition and its detectability at future observations. Our discussions motivate further studies on phase transitions in composite Higgs models with the use of lattice simulations.

\U0001d4a9 = 1 SCFTs from F-theory on Orbifolds

We study four-dimensional superconformal field theories living on the worldvolume of D3 branes probing minimally-supersymmetric F-theory backgrounds, focusing on the case of orbi-orientifold setups with and without 7-branes. We observe that these theories are closely related to compactifications of six-dimensional \U0001d4a9 = (1, 0) theories on a torus with flux, where the flux quanta is mapped in Type IIB to the defining data of the orbifold group. We analyze the cases of class \U0001d4aek theories as well as of compactifications of the E-string and of orbi-instanton theories. We also classify \U0001d4ae-fold configurations in F-theory preserving minimal supersymmetry in four dimensions and their mass deformations.

The Higgs condensate as a quantum liquid: A critical comparison with observations

The triviality of four-dimensional scalar quantum field theories poses challenging problems to the usually adopted perturbative implementation of the Higgs mechanism. In the first part of the paper, we compare the triviality scenario and the renormalized two-loop perturbation theory to precise and extensive results from nonperturbative numerical simulations of the real scalar field theory on the lattice. The proposal of triviality and spontaneous symmetry breaking turns out to be in good agreement with numerical simulations, while the renormalized perturbative approach seems to suffer significant deviations from the numerical simulation results. In the second part of the paper, we try to illustrate how the triviality of four-dimensional scalar field theory leads, nevertheless, to the spontaneous symmetry breaking in the scalar sector of the Standard Model. We show how triviality allows us to develop a physical picture of the Higgs mechanism in the Standard Model. We suggest that the Higgs condensate behaves like a relativistic quantum liquid leading to the prevision of two Higgs bosons. The light Higgs boson resembles closely the new LHC narrow resonance at 125 GeV. The heavy Higgs boson is a rather broad resonance with mass of about 730 GeV. We critically compare our proposal to the complete LHC Run 2 data collected by the ATLAS and CMS Collaborations. We do not find convincingly evidences of the heavy Higgs boson in the ATLAS datasets. On the other hand, the CMS full Run 2 data display evidences of a heavy Higgs boson in the main decay modes [Formula: see text], while in the preliminary Run 2 data there are hints of the decays [Formula: see text] in the golden channel. We also critically discuss plausible reasons for the discrepancies between the two LHC experiments.

Supersymmetric AdS Solitons, Ground States, and Phase Transitions in Maximal Gauged Supergravity

We review some recent soliton solutions in a class of four-dimensional supergravity theories. The latter can be obtained from black hole solutions by means of a double Wick rotation. For special values of the parameters, the new configurations can be embedded in the gauged maximal N=8 theory and uplifted in the higher-dimensional D=11 theory. We also consider BPS soliton solutions, preserving a certain fraction of supersymmetry.

Feynman diagrams in four-dimensional holomorphic theories and the Operatope

We study a class of universal Feynman integrals which appear in four-dimensional holomorphic theories. We recast the integrals as the Fourier transform of a certain polytope in the space of loop momenta (a.k.a. the “Operatope”). We derive a set of quadratic recursion relations which appear to fully determine the final answer. Our strategy can be applied to a very general class of twisted supersymmetric quantum field theories.

Near-extremal limits of de Sitter black holes

We analyze the thermodynamic response near extremality of charged black holes in four-dimensional Einstein-Maxwell theory with a positive cosmological constant. The latter exhibit three different extremal limits, dubbed cold, Nariai and ultracold configurations, with near-horizon geometries AdS2 × S2, dS2 × S2, Mink2 × S2, respectively. For each of these three cases we analyze small deformations away from extremality, and contrast their response. We also construct the effective two-dimensional theory, obtained by dimensional reduction, that captures these features and provide a more detailed analysis of the perturbations around the near-horizon geometry for each case. Our results for the ultracold case in particular show an interesting interplay between the entropy variation and charge variation, realizing a different response in comparison to the other two near-extremal limits.

Effective approach to the Antoniadis-Mottola model: quantum decoupling of the higher derivative terms

We explore the decoupling of massive ghost mode in the 4D (four-dimensional) theory of the conformal factor of the metric. The model was introduced by Antoniadis and Mottola in [1] and can be regarded as a close analog of the fourth-derivative quantum gravity. The analysis of the derived one-loop nonlocal form factors includes their asymptotic behavior in the UV and IR limits. In the UV (high energy) domain, our results reproduce the Minimal Subtraction scheme-based beta functions of [1]. In the IR (i.e., at low energies), the diagrams with massive ghost internal lines collapse into tadpole-type graphs without nonlocal contributions and become irrelevant. On the other hand, those structures that contribute to the running of parameters of the action and survive in the IR, are well-correlated with the divergent part (or the leading in UV contributions to the form factors), coming from the effective low-energy theory of the conformal factor. This effective theory describes only the light propagating mode. Finally, we discuss whether these results may shed light on the possible running of the cosmological constant at low energies.

Dirac-Born-Infeld counter-term and black hole thermodynamics

Abstract We revisit the Dirac-Born-Infeld–like boundary counter-term for the four-dimensional theory of gravity. We show that it correctly executes complete background subtraction for both asymptotically Anti-de Sitter and asymptotically flat geometries. With an appropriate choice of ensemble, we reproduce dyonic black hole thermodynamics with both types of asymptotics by studying local thermodynamics on the cut-off surface.

Kac-Moody symmetry in the light front of gauge theories

We discuss the emergence of a new symmetry generator in a Hamiltonian realisation of four-dimensional gauge theories in the flat space foliated by retarded (advanced) time. It generates an asymptotic symmetry that acts on the asymptotic fields in a way different from the usual large gauge transformations. The improved canonical generators, corresponding to gauge and asymptotic symmetries, form a classical Kac-Moody charge algebra with a non-trivial central extension. In particular, we describe the case of electromagnetism, where the charge algebra is the U(1) current algebra with a level proportional to the coupling constant of the theory, κ = 4π2/e2. We construct bilinear generators yielding Virasoro algebras on the null boundary. We also provide a non-Abelian generalization of the previous symmetries by analysing the evolution of Yang-Mills theory in Bondi coordinates.

Toward minimal composite Higgs models from regular geometries in bottom-up holography

We study a bottom-up, holographic description of a field theory yielding the spontaneous breaking of an approximate $SO(5)$ global symmetry to its $SO(4)$ subgroup. The weakly coupled, six-dimensional gravity dual has regular geometry. One of the dimensions is compactified on a circle that shrinks smoothly to zero size at a finite value of the holographic direction, hence introducing a physical scale in a way that mimics the effect of confinement in the dual four-dimensional field theory. We study the spectrum of small fluctuations of the bulk fields carrying $SO(5)$ quantum numbers, which can be interpreted as spin-0 and spin-1 bound states in the dual field theory. This work supplements an earlier publication focused only on the $SO(5)$ singlet states. We explore the parameter space of the theory, paying particular attention to composite states that have the right quantum numbers to be identified as pseudo-Nambu-Goldstone bosons (PNGBs). We find that in this model the PNGBs are generally heavy, with masses of the same order as other bound states, indicating the presence of a sizeable amount of explicit symmetry breaking in the field-theory side. Nevertheless, we also find a qualitatively new, unexpected result. When the dimension of the field-theory operator inducing $SO(5)$ breaking is close to half the space-time dimensionality, there exists a region of parameter space in which the PNGBs and the lightest scalar are both parametrically light in comparison to all other bound states of the field theory. Although this region is known to yield metastable classical backgrounds, this finding might be relevant to model building in the composite Higgs context.

TT¯ deformed soft theorem

In this paper, we derive a $T\bar{T}$ deformed soft graviton theorem in the context of celestial holography. As a concrete example, it illustrates that a two-dimensional irrelevant deformation can be applied to a four-dimensional theory at the level of amplitudes. We argue that the $T\bar{T}$ deformation has a close relation to the loop-correction from the amplitude side which could provide an alternative way to construct an ultraviolet complete quantum theory of gravity.