Four-dimensional Field Theory Research Articles

N = 2 Orbi-S-Folds

We introduce a new class of non-compact backgrounds of Type IIB string theory preserving eight supercharges by combining S-folds and non-perturbative 7-branes wrapping orbifolds, and study the four-dimensional superconformal field theories arising at low energy on D3-branes probing them. We draw a precise correspondence between this setup and the torus compactification of six-dimensional orbi-instanton theories with a Stiefel-Whitney twist, and use it to determine the main features of such strongly-coupled systems, like central charges, spectra of Coulomb-branch operators, networks of Higgs-branch flows. Finally, with the aim to improve our understanding of the landscape of N = 2 superconformal field theories, and possibly to extend their classification beyond rank two, we provide a detailed catalogue of all the rank-three theories that our framework gives access to.

Non-invertible flavor symmetries in magnetized extra dimensions

We discuss non-invertible symmetries in toroidal compactifications of higher dimensional Yang-Mills theory with magnetic fluxes, which can be regarded as an effective action of type IIB string theory with magnetized D-branes. Specifically, we derive fusion rules of discrete isometry operators, which are invariant under the ℤN orbifold twist. It turns out that degenerate chiral zero-modes non-trivially transform under the non-invertible symmetries in the context of quantum mechanics. Hence, non-invertible symmetries correspond to flavor symmetries of chiral zero modes and determine their flavor structure. We explicitly show the representations and selection rules of chiral zero modes on their wave functions. These zero modes may correspond to generations of quarks and leptons in four-dimensional low-energy effective field theory.

Light-ray sum rules and the c-anomaly

In a four-dimensional quantum field theory that flows between two fixed points under the renormalization group, the change in the conformal anomaly ∆a has been related to the average null energy. We extend this result to derive a sum rule for the other anomaly coefficient, ∆c, in terms of the stress tensor three-point function. While the sum rule for ∆a is an expectation value of the averaged null energy operator, and therefore positive, the result for ∆c involves the off-diagonal matrix elements, so it does not have a fixed sign.

Gravitational duals from equations of state

Holography relates gravitational theories in five dimensions to four-dimensional quantum field theories in flat space. Under this map, the equation of state of the field theory is encoded in the black hole solutions of the gravitational theory. Solving the five-dimensional Einstein’s equations to determine the equation of state is an algorithmic, direct problem. Determining the gravitational theory that gives rise to a prescribed equation of state is a much more challenging, inverse problem. We present a novel approach to solve this problem based on physics-informed neural networks. The resulting algorithm is not only data-driven but also informed by the physics of the Einstein’s equations. We successfully apply it to theories with crossovers, first- and second-order phase transitions.

Anomalies in string-inspired nonlocal extensions of QED

We investigate anomalies in the class of nonlocal field theories that have been proposed as an ultraviolet completion of four-dimensional quantum field theory with generalizing the kinetic energy operators to an infinite series of higher derivatives inspired by the string field theory and ghost-free nonlocal approaches to quantum gravity. We explicitly calculate the vector and chiral anomalies in a string-inspired nonlocal extension of QED. We show that the vector anomaly vanishes as required by gauge invariance and the Ward identity. On the other hand, although the chiral anomaly vanishes to the leading order with massless fermions, it nonetheless does not vanish with the massive fermions and we calculate it to the leading order in the scale of nonlocality. We also calculate the nonlocal vector and axial currents explicitly and present an illustrative example by applying our results to the decay of π0→γγ. Published by the American Physical Society 2024

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.

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.

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.

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.

Holographic thermal correlators from supersymmetric instantons

We present an exact formula for the thermal scalar two-point function in four-dimensional holographic conformal field theories. The problem of finding it reduces to the analysis of the wave equation on the AdS-Schwarzschild background. The two-point function is computed from the connection coefficients of the Heun equation, which can be expressed in terms of the Nekrasov-Shatashvili partition function of an SU(2)SU(2) supersymmetric gauge theory with four fundamental hypermultiplets. The result is amenable to numerical evaluation upon truncating the number of instantons in the convergent expansion of the partition function. We also examine it analytically in various limits. At large spin the instanton expansion of the thermal two-point function directly maps to the light-cone bootstrap analysis of the heavy-light four-point function. Using this connection, we compute the OPE data of heavy-light double-twist operators. We compare our prediction to the perturbative results available in the literature and find perfect agreement.

Causality constraints on corrections to Einstein gravity

We study constraints from causality and unitarity on 2 → 2 graviton scattering in four-dimensional weakly-coupled effective field theories. Together, causality and unitarity imply dispersion relations that connect low-energy observables to high-energy data. Using such dispersion relations, we derive two-sided bounds on gravitational Wilson coefficients in terms of the mass M of new higher-spin states. Our bounds imply that gravitational interactions must shut off uniformly in the limit G → 0, and prove the scaling with M expected from dimensional analysis (up to an infrared logarithm). We speculate that causality, together with the non-observation of gravitationally-coupled higher spin states at colliders, severely restricts modifications to Einstein gravity that could be probed by experiments in the near future.

Operator spectroscopy for 4D SCFTs with a=c

We study a rich set of four-dimensional superconformal field theories with both central charges identical: $a=c$. These are constructed via the diagonal $\mathcal{N}=2$ or $\mathcal{N}=1$ gauging of the flavor symmetry $G$ of a collection of $\mathcal{N}=2$ Argyres-Douglas theories of type ${\mathcal{D}}_{p}(G)$, with or without adjoint chiral multiplets, in 2106.12579 and 2111.12092. We compute superconformal indices of some theories where the rank of $G$ is low, performing a refined test for unitarity, and further determine the relevant and marginal operator content in detail. We find that most of these theories flow to interacting superconformal field theories with $a=c$ in the infrared.

Effective action of a self-interacting scalar field on brane

In extra dimensional theories, the four-dimensional field theory is reduced from a fundamental field theory in the bulk spacetime by integrating the extra dimensional part. In this paper we investigate the effective action of a self-interacting scalar field on a brane in the five-dimensional thick braneworld scenario. We consider two typical thick brane solutions and obtain the Pöschl–Teller and harmonic potentials of the Kaluza–Klein (KK) modes, respectively. The analytical mass spectra and wave functions along extra dimension of the KK modes are obtained. Further, the effective coupling constant between different KK particles, cross section, and decay rate for some processes of the KK particles are related to the fundamental coupling in five dimensions and the new physics energy scale. Some interesting properties of these interactions are found with these calculations. The KK particles with higher mode have longer lifetime, and they almost do not interact with ordinary matter on the brane if their mode numbers are large enough. Thus, these KK particles with higher modes might be a candidate of dark matter.

Heterotic quantum cohomology

It is believed, but not demonstrated, that the large radius massless spectrum of a heterotic string theory compactified to four-dimensional Minkowski space should obey equations that split into ‘F-terms’ and ‘D-terms’ in ways analogous to that of four-dimensional supersymmetric field theories. This is not easy to do directly as string theory is first quantised. Nonetheless, in this paper we demonstrate this splitting. We construct an operator overline{mathcal{D}} whose kernel amounts to deformations solving ‘F-term’ type equations. In many previous works in this field, the spin connection is treated as an independent degree of freedom (and so is spurious or fake); here our results apply on the physical moduli space in which these fake degrees of freedom are eliminated. We utilise the moduli space metric, constructed in previous work, to define an adjoint operator overline{mathcal{D}} †. The kernel of overline{mathcal{D}} † amounts to ‘D-term’ type equations. Put together, we show there is a overline{mathcal{D}} -operator in which the massless spectrum are harmonic representatives of overline{mathcal{D}} . We conjecture that one could better study the moduli space of heterotic theories by studying the corresponding cohomology, a natural counterpart to studying the overline{partial} -cohomology groups relevant to moduli of Calabi-Yau manifolds.

Tameness, Strings, and the Distance Conjecture

The Distance Conjecture states that an infinite tower of modes becomes exponentially light when approaching an infinite distance point in field space. We argue that the inherent path-dependence of this statement can be addressed when combining the Distance Conjecture with the recent Tameness Conjecture. The latter asserts that effective theories are described by tame geometry and implements strong finiteness constraints on coupling functions and field spaces. By exploiting these tameness constraints we argue that the region near the infinite distance point admits a decomposition into finitely many sectors in which path-independent statements for the associated towers of states can be established. We then introduce a more constrained class of tame functions with at most polynomial asymptotic growth and argue that they suffice to describe the known string theory effective actions. Remarkably, the multi-field dependence of such functions can be reconstructed by one-dimensional linear test paths in each sector near the boundary. In four-dimensional effective theories, these test paths are traced out as a discrete set of cosmic string solutions. This indicates that such cosmic string solutions can serve as powerful tool to study the near-boundary field space region of any four-dimensional effective field theory. To illustrate these general observations we discuss the central role of tameness and cosmic string solutions in Calabi-Yau compactifications of Type IIB string theory.

Double copy for massive scalar field theories

We explore extensions of the double copy to massive theories and find a new cubic theory with a local double copy. We consider the nonlinear sigma model and the special galileon theory, massless versions of which are known to be related through the double copy. We show that by performing a Kaluza-Klein reduction of these theories from five dimensions down to four, a double copy relation exists between the resulting massive four-dimensional scalar field theories. This requires the vanishing contribution of new galileon terms arising in high dimensions. We further explore if other interactions that do not arise from a dimensional reduction of the nonlinear sigma model could be double copied and find a new cubic interaction which satisfies the BCJ relations up to 5-point amplitudes.

Bootstrapping a stress-tensor form factor through eight loops

We bootstrap the three-point form factor of the chiral stress-tensor multiplet in planar mathcal{N} = 4 supersymmetric Yang-Mills theory at six, seven, and eight loops, using boundary data from the form factor operator product expansion. This may represent the highest perturbative order to which multi-variate quantities in a unitary four-dimensional quantum field theory have been computed. In computing this form factor, we observe and employ new restrictions on pairs and triples of adjacent letters in the symbol. We provide details about the function space required to describe the form factor through eight loops. Plotting the results on various lines provides striking numerical evidence for a finite radius of convergence of perturbation theory. By the principle of maximal transcendentality, our results are expected to give the highest weight part of the gg → Hg and H → ggg amplitudes in the heavy-top limit of QCD through eight loops. These results were also recently used to discover a new antipodal duality between this form factor and a six-point amplitude in the same theory.