Three-dimensional Field Theory Research Articles

An analytical solution of eccentric transverse deflection in rigid-plastic solids

For a rigid-plastic solid obeying Tresca's yield criterion which deforms by the mechanism of extended slip, it conforms to the principle of rotation-rate continuity if the yield shear stress remains constant. It has been proved on this basis that the divergence of the strain-rate tensor is zero and the velocity vector field obeys the Laplace equation in the deformation region. This property can lead to two general solutions, one is derived into three-dimensional slip-line field theory; the other is applied to solve the problem of transverse deflection of a clamped plate deflected by a flat-ended rigid punch. For concentric loading conditions explicit analytical solutions can be obtained directly, while for eccentric loading conditions the method of fundamental solutions (MFS) is applied in the deformation region which is seen as a doubly-connected domain obeying the harmonic equation. The punching force needed for the deflection and strain components are then calculated. It has been obtained that the contour lines and the lines of steepest descent are two principle lines of any point in the deformation region, so the method of steepest descent is used to depict the trajectories of the principle lines. Numerical calculations have been made using commercial finite element software ANSYS-LSDYNA. It turns out that the results obtained from numerical calculations fit quite well with the analytical results based on the principle of rotation-rate continuity and MFS. Finally, NURBS curves and Coons surface are used to construct the configurations of slip-planes in this problem, where the normal of slip-planes and the planes on which the two families of slip-lines located are both curved.

A computational scheme of pKa values based on the three-dimensional reference interaction site model self-consistent field theory coupled with the linear fitting correction scheme.

A scheme for quantitatively computing the acid dissociation constant, pKa, of hydrated molecules is proposed. It is based on the three-dimensional reference interaction site model self-consistent field (3D-RISM-SCF) theory coupled with the linear fitting correction (LFC) scheme. In LFC/3D-RISM-SCF, pKa values of target molecules are evaluated using the Gibbs energy difference between the protonated and unprotonated states calculated by 3D-RISM-SCF and the parameters fitted by the LFC scheme to the experimental values of training set systems. The pKa values computed by LFC/3D-RISM-SCF show quantitative agreement with the experimental data.

The Holographic F Theorem

The F theorem states that, for a unitary three dimensional quantum field theory, the F quantity defined in terms of the partition function on a three sphere is positive, stationary at fixed point and decreases monotonically along a renormalization group flow. We construct holographic renormalization group flows corresponding to relevant deformations of three-dimensional conformal field theories on spheres, working to quadratic order in the source. For these renormalization group flows, the F quantity at the IR fixed point is always less than F at the UV fixed point, but F increases along the RG flow for deformations by operators of dimension between 3/2 and 5/2. Therefore the strongest version of the F theorem is in general violated.

Rahman\u2019s Biorthogonal Rational Functions and Superconformal Indices

We study biorthogonal functions related to basic hypergeometric integrals with coupled continuous and discrete components. Such integrals appear as superconformal indices for three-dimensional quantum field theories and also in the context of solvable lattice models. We obtain explicit biorthogonal systems given by products of two of Rahman’s biorthogonal rational {}_{10}W_9-functions or their degenerate cases. We also give new bilateral extensions of the Jackson and q-Saalschütz summation formulas and new continuous and discrete biorthogonality measures for Rahman’s functions.

Numerical estimation of structure constants in the three-dimensional Ising conformal field theory through Markov chain uv sampler.

Herdeiro and Doyon [Phys. Rev. E 94, 043322 (2016)2470-004510.1103/PhysRevE.94.043322] introduced a numerical recipe, dubbed uv sampler, offering precise estimations of the conformal field theory (CFT) data of the planar two-dimensional (2D) critical Ising model. It made use of scale invariance emerging at the critical point in order to sample finite sublattice marginals of the infinite plane Gibbs measure of the model by producing holographic boundary distributions. The main ingredient of the Markov chain Monte Carlo sampler is the invariance under dilation. This paper presents a generalization to higher dimensions with the critical 3D Ising model. This leads to numerical estimations of a subset of the CFT data-scaling weights and structure constants-through fitting of measured correlation functions. The results are shown to agree with the recent most precise estimations from numerical bootstrap methods [Kos, Poland, Simmons-Duffin, and Vichi, J. High Energy Phys. 08 (2016) 03610.1007/JHEP08(2016)036].

Supersymmetric Galileons and auxiliary fields in 2+1 dimensions

In this work we study various aspects of supersymmetric three-dimensional higher-derivative field theories. We classify all possible models without derivative terms in the auxiliary field of the fermionic sector and find that scalar field theories of the form $P(X,\phi)$, where $X=-(\partial\phi)^2/2$, belong to this kind of models. A ghost-free supersymmetric extension of Galileon models is found in three spacetime dimensions. Finally, the auxiliary field problem is discussed.

Effective potential of the three-dimensional Ising model: The pseudo-ϵ expansion study

The ratios R2k of renormalized coupling constants g2k that enter the effective potential and small-field equation of state acquire the universal values at criticality. They are calculated for the three-dimensional scalar λϕ4 field theory (3D Ising model) within the pseudo-ϵ expansion approach. Pseudo-ϵ expansions for the critical values of g6, g8, g10, R6=g6/g42, R8=g8/g43 and R10=g10/g44 originating from the five-loop renormalization group (RG) series are derived. Pseudo-ϵ expansions for the sextic coupling have rapidly diminishing coefficients, so addressing Padé approximants yields proper numerical results. Use of Padé–Borel–Leroy and conformal mapping resummation techniques further improves the accuracy leading to the values R6⁎=1.6488 and R6⁎=1.6490 which are in a brilliant agreement with the result of advanced lattice calculations. For the octic coupling the numerical structure of the pseudo-ϵ expansions is less favorable. Nevertheless, the conform-Borel resummation gives R8⁎=0.868, the number being close to the lattice estimate R8⁎=0.871 and compatible with the result of 3D RG analysis R8⁎=0.857. Pseudo-ϵ expansions for R10⁎ and g10⁎ are also found to have much smaller coefficients than those of the original RG series. They remain, however, fast growing and big enough to prevent obtaining fair numerical estimates.

Asymptotic safety in three-dimensional SU(2) group field theory: evidence in the local potential approximation

We study the functional renormalization group of a three-dimensional tensorial group field theory (GFT) with gauge group . This model generates (generalized) lattice gauge theory amplitudes, and is known to be perturbatively renormalizable up to order 6 melonic interactions. We consider a series of truncations of the exact Wetterich–Morris equation, which retain increasingly many perturbatively irrelevant melonic interactions. This tensorial analogue of the ordinary local potential approximation allows us to investigate the existence of non-perturbative fixed points of the renormalization group flow. Our main finding is a candidate ultraviolet fixed point, whose qualitative features are reproduced in all the truncations we have checked (with up to order 12 interactions). This may be taken as evidence for an ultraviolet completion of this GFT in the sense of asymptotic safety. Moreover, this fixed point has a single relevant direction, which suggests the presence of two distinct infrared phases. Our results generally support the existence of GFT phases of the condensate type, which have recently been conjectured and applied to quantum cosmology and black holes.

Liquid-gas phase transitions and CK symmetry in quantum field theories

A general field-theoretic framework for the treatment of liquid-gas phase transitions is developed. Starting from a fundamental four-dimensional field theory at nonzero temperature and density, an effective three-dimensional field theory with a sign problem is derived. Although charge conjugation $\mathcal{C}$ is broken at finite density, there remains a symmetry under $\mathcal{CK}$, where $\mathcal{K}$ is complex conjugation. We consider four models: relativistic fermions, nonrelativistic fermions, static fermions and classical particles. The thermodynamic behavior is extracted from $\mathcal{CK}$-symmetric complex saddle points of the effective field theory at tree level. The relativistic and static fermions show a liquid-gas transition, manifesting as a first-order line at low temperature and high density, terminated by a critical end point. In the cases of nonrelativistic fermions and classical particles, we find no first-order liquid-gas transitions at tree level. The mass matrix controlling the behavior of correlation functions is obtained from fluctuations around the saddle points. Due to the $\mathcal{CK}$ symmetry of the models, the eigenvalues of the mass matrix can be complex. This leads to the existence of disorder lines, which mark the boundaries where the eigenvalues go from purely real to complex. The regions where the mass matrix eigenvalues are complex are associated with the critical line. In the case of static fermions, a powerful duality between particles and holes allows for the analytic determination of both the critical line and the disorder lines. Depending on the values of the parameters, either zero, one or two disorder lines are found. Numerical results for relativistic fermions give a very similar picture.

Euclidean M-theory background dual to a three-dimensional scale-invariant field theory without conformal invariance

We show that eleven dimensional supergravity in Euclidean signature admits an exact classical solution with isometry corresponding to a three dimensional scale invariant field theory without conformal invariance. We also construct the holographic renormalization group flow that connects the known UV conformal fixed point and the new scale invariant but not conformal fixed point. In view of holography, the existence of such classical solutions suggests that the topologically twisted M2-brane gauge theory possesses a scale invariant but not conformal phase.

Bayesian approach for calibrating transformation model from spatially varied CPT data to regular geotechnical parameter

Cone Penetration Test (CPT) is widely utilized to gain regular geotechnical parameters such as compression modulus, cohesion coefficient and internal friction angle by transformation model in the site investigation. However, it is challenging to obtain simultaneously the unknown coefficients and error of a transformation model, given the intrinsic uncertainty (i.e., spatial variability) of geomaterial and the epistemic uncertainty of geotechnical investigation. A Bayesian approach is therefore proposed calibrating the transformation model based on spatial random field theory. The approach consists of three key elements: (1) three-dimensional anisotropic spatial random field theory; (2) classifications of measurement and error, and the uncertainty propagation diagram of geotechnical investigation; and (3) the unknown coefficients and error calibration of the transformation model given Bayesian inverse modeling method. The massive penetration resistance data from CPT, which is denoted as a spatial random field variable to account for the spatial variability of soil, are classified as type A data. Meanwhile, a few laboratory test data such as the compression modulus are defined as type B data. Based on the above two types of data, the unknown coefficients and error of the transformation model are inversely calibrated with consideration of intrinsic uncertainty of geomaterial, epistemic uncertainties such as measurement errors, prior knowledge uncertainty of transformation model itself, and computing uncertainties of statistical parameters as well as Bayesian method. Baseline studying indicates the proposed approach is applicable to calibrate the transformation model between CPT data and regular geotechnical parameter within spatial random field theory. Next, the calibrated transformation model was compared with classical linear regression in cross-validation, and then it was implemented at three-dimensional site characterization of the background project.

Higher spin realization of the DS/CFT correspondence

We conjecture that Vasiliev’s theory of higher spin gravity in four-dimensional de Sitter space (dS4) is holographically dual to a three-dimensional conformal field theory (CFT3) living on the spacelike boundary of dS4 at future timelike infinity. The CFT3 is the Euclidean Sp(N) vector model with anticommuting scalars. The free CFT3 flows under a double-trace deformation to an interacting CFT3 in the IR. We argue that both CFTs are dual to Vasiliev dS4 gravity but with different future boundary conditions on the bulk scalar field. Our analysis rests heavily on analytic continuations of bulk and boundary correlators in the proposed duality relating the O(N) model with Vasiliev gravity in AdS4.

Stability data, irregular connections and tropical curves

We study a class of meromorphic connections ∇(Z) on P1, parametrised by the central charge Z of a stability condition, with values in a Lie algebra of formal vector fields on a torus. Their definition is motivated by the work of Gaiotto, Moore and Neitzke on wall-crossing and three-dimensional field theories. Our main results concern two limits of the families ∇(Z) as we rescale the central charge Z → RZ. In the R → 0 conformal limit we recover a version of the connections introduced by Bridgeland and Toledano Laredo (and so the Joyce holomorphic generating functions for enumerative invariants), although with a different construction yielding new explicit formulae. In the R → ∞ large complex structure limit the connections ∇(Z) make contact with the Gross-Pandharipande-Siebert approach to wall-crossing based on tropical geometry. Their flat sections display tropical behaviour, and also encode certain tropical/relative Gromov-Witten invariants.

Time-sliced perturbation theory for large scale structure I: general formalism

We present a new analytic approach to describe large scale structure formation in the mildly non-linear regime. The central object of the method is the time-dependent probability distribution function generating correlators of the cosmological observables at a given moment of time. Expanding the distribution function around the Gaussian weight we formulate a perturbative technique to calculate non-linear corrections to cosmological correlators, similar to the diagrammatic expansion in a three-dimensional Euclidean quantum field theory, with time playing the role of an external parameter. For the physically relevant case of cold dark matter in an Einstein-de Sitter universe, the time evolution of the distribution function can be found exactly and is encapsulated by a time-dependent coupling constant controlling the perturbative expansion. We show that all building blocks of the expansion are free from spurious infrared enhanced contributions that plague the standard cosmological perturbation theory. This paves the way towards the systematic resummation of infrared effects in large scale structure formation. We also argue that the approach proposed here provides a natural framework to account for the influence of short-scale dynamics on larger scales along the lines of effective field theory.

On level crossing in conformal field theories

We study the properties of operators in a unitary conformal field theory whose scaling dimensions approach each other for some values of the parameters and satisfy von Neumann-Wigner non-crossing rule. We argue that the scaling dimensions of such operators and their OPE coefficients have a universal scaling behavior in the vicinity of the crossing point. We demonstrate that the obtained relations are in a good agreement with the known examples of the level-crossing phenomenon in maximally supersymmetric $\mathcal N=4$ Yang-Mills theory, three-dimensional conformal field theories and QCD.

Theoretical analysis of complex formation of p-carboxybenzeneboronic acid with a monosaccharide

Changes in the acid dissociation constant, pKa, of p-carboxybenzeneboronic acid (PCBA) upon complex formation with monosaccharide are considered by using the three-dimensional reference interaction site model self-consistent field theory. The pKa of PCBA is lowered through complex formation, which is consistent with experimental observations. Free energy component analysis of the dissociation reaction was performed to investigate the details of the contribution to the pKa shift. The magnitudes of the changes in both the electronic energy and the solvation free energy were smaller for the PCBA-complex than for PCBA. These smaller changes can be attributed to the delocalization of the excess charge and to a reduction of the solvent-accessible area near the boric acid group because of the steric bulk of the monosaccharide.

A Trace for Bimodule Categories

We study a 2-functor that assigns to a bimodule category over a finite \(\Bbbk \)-linear tensor category a \(\Bbbk \)-linear abelian category. This 2-functor can be regarded as a category-valued trace for 1-morphisms in the tricategory of finite tensor categories. It is defined by a universal property that is a categorification of Hochschild homology of bimodules over an algebra. We present several equivalent realizations of this 2-functor and show that it has a coherent cyclic invariance. Our results have applications to categories associated to circles in three-dimensional topological field theories with defects. This is made explicit for the subclass of Dijkgraaf-Witten topological field theories.

Holographic mutual information for singular surfaces

We study corner contributions to holographic mutual information for entangling regions composed of a set of disjoint sectors of a single infinite circle in three-dimensional conformal field theories. In spite of the UV divergence of holographic mutual information, it exhibits a first order phase transition. We show that tripartite information is also divergent for disjoint sectors, which is in contrast with the well-known feature of tripartite information being finite even when entangling regions share boundaries. We also verify the locality of corner effects by studying mutual information between regions separated by a sharp annular region. Possible extensions to higher dimensions and hyperscaling violating geometries is also considered for disjoint sectors.

Universal entanglement for higher dimensional cones

The entanglement entropy of a generic $d$-dimensional conformal field theory receives a regulator independent contribution when the entangling region contains a (hyper)conical singularity of opening angle $\Omega$, codified in a function $a^{(d)}(\Omega)$. In arXiv:1505.04804, we proposed that for three-dimensional conformal field theories, the coefficient $\sigma$ characterizing the smooth surface limit of such contribution ($\Omega\rightarrow \pi$) equals the stress tensor two-point function charge $C_{ T}$, up to a universal constant. In this paper, we prove this relation for general three-dimensional holographic theories, and extend the result to general dimensions. In particular, we show that a generalized coefficient $\sigma^{ (d)}$ can be defined for (hyper)conical entangling regions in the almost smooth surface limit, and that this coefficient is universally related to $C_{ T}$ for general holographic theories, providing a general formula for the ratio $\sigma^{ (d)}/C_{ T}$ in arbitrary dimensions. We conjecture that the latter ratio is universal for general CFTs. Further, based on our recent results in arXiv:1507.06997, we propose an extension of this relation to general R\'enyi entropies, which we show passes several consistency checks in $d=4$ and $d=6$.

Modeling the Adsorption of Rheology Modifiers onto Latex Particles Using Coarse-Grained Molecular Dynamics (CG-MD) and Self-Consistent Field Theory (SCFT)

We model the adsorption of hydrophobically ethoxylated urethane (HEUR) thickeners onto two hydrophobic surfaces separated by a 50 nm gallery using coarse-grained molecular dynamics (CG-MD) with implicit solvent and three-dimensional self-consistent field theory (SCFT) with explicit solvent. The CG-MD simulations can be readily extended to encompass very long HEUR chains (up to 540 EO groups) but cannot with current computer speed simulate adsorption of HEURs with hydrophobes longer than 12 carbons (C12). The SCFT method can readily simulate HEURs with longer, C16, hydrophobes but has a greater challenge simulating very long EO chains. For HEURs with 180 EO units and C8 and C12 hydrophobes, both methods can be applied, allowing a combination of the two methods to span much of the parameter space of interest to experimentalists. It is demonstrated that depending on the hydrophobe strength and the HEUR concentration, HEUR chains can adsorb to the surfaces directly or indirectly (as adsorbed micelles or admic...