4D Theory Research Articles

Elliptic genus derivation of 4d holomorphic blocks

We study elliptic vortices on ℂ × T2 by considering the 2d quiver gauge theory describing their moduli spaces. The elliptic genus of these moduli spaces is the elliptic version of vortex partition function of the 4d theory. We focus on two examples: the first is a mathcal{N} = 1, U(N ) gauge theory with fundamental and anti-fundamental matter; the second is a mathcal{N} = 2, U(N ) gauge theory with matter in the fundamental representation. The results are instances of 4d “holomorphic blocks” into which partition functions on more complicated surfaces factorize. They can also be interpreted as free-field representations of elliptic Virasoro algebrae.

Five-dimensional fermionic Chern-Simons theory

We study 5d fermionic CS theory with a fermionic 2-form gauge potential. This theory can be obtained from 5d maximally supersymmetric YM theory by performing the maximal topological twist. We put the theory on a five-manifold and compute the partition function. We find that it is a topological quantity, which involves the Ray-Singer torsion of the five-manifold. For abelian gauge group we consider the uplift to the 6d theory and find a mismatch between the 5d partition function and the 6d index, due to the nontrivial dimensional reduction of a selfdual two-form gauge field on a circle. We also discuss an application of the 5d theory to generalized knots made of 2d sheets embedded in 5d.

Green-Schwarz automorphisms and 6D SCFTs

All known interacting 6D superconformal field theories (SCFTs) have a tensor branch which includes anti-chiral two-forms and a corresponding lattice of string charges. Automorphisms of this lattice preserve the Dirac pairing and specify discrete global and gauge symmetries of the 6D theory. In this paper we compute this automorphism group for 6D SCFTs. This discrete data determines the geometric structure of the moduli space of vacua. Upon compactification, these automorphisms generate Seiberg-like dualities, as well as additional theories in discrete quotients by the 6D global symmetries. When a perturbative realization is available, these discrete quotients correspond to including additional orientifold planes in the string construction.

6d surface defects from massive type IIA

We present a new BPS flow within minimal mathcal{N}=1 supergravity in seven dimensions describing a warped AdS3 background supported by a “dyonic” profile of the three-form. Furthermore, we discuss the holographic interpretation of the above solution in terms of a defect SCFT2 inside the 6d (1, 0) theory dual to the AdS in the asymptotic region. Finally we provide the brane picture of the aforementioned defect CFT as D2- and wrapped D4-branes ending on a D6 - NS5 - D8 funnel in massive type IIA string theory.

A new quasi-3D sinusoidal shear deformation theoryfor functionally graded plates

In this paper, a new quasi-3D sinusoidal shear deformation theory for functionally graded (FG) plates is proposed. The theory considers both shear deformation and thickness-stretching influences by a trigonometric distribution of all displacements within the thickness, and respects the stress-free boundary conditions on the upper and lower faces of the plate without employing any shear correction coefficient. The advantage of the proposed model is that it posses a smaller number of variables and governing equations than the existing quasi-3D models, but its results compare well with those of 3D and quasi-3D theories. This benefit is due to the use of undetermined integral unknowns in the displacement field of the present theory. By employing the Hamilton principle, equations of motion are obtained in the present formulation. Closed-form solutions for bending and free vibration problems are determined for simply supported plates. Numerical examples are proposed to check the accuracy of the developed theory.

Time-reversal breaking in QCD4, walls, and dualities in 2 + 1 dimensions

We study SU(N ) Quantum Chromodynamics (QCD) in 3+1 dimensions with Nf degenerate fundamental quarks with mass m and a θ-parameter. For generic m and θ the theory has a single gapped vacuum. However, as θ is varied through θ = π for large m there is a first order transition. For Nf = 1 the first order transition line ends at a point with a massless η′ particle (for all N ) and for Nf> 1 the first order transition ends at m = 0, where, depending on the value of Nf , the IR theory has free Nambu-Goldstone bosons, an interacting conformal field theory, or a free gauge theory. Even when the 4d bulk is smooth, domain walls and interfaces can have interesting phase transitions separating different 3d phases. These turn out to be the phases of the recently studied 3d Chern-Simons matter theories, thus relating the dynamics of QCD4 and QCD3, and, in particular, making contact with the recently discussed dualities in 2+1 dimensions. For example, when the massless 4d theory has an SU(Nf ) sigma model, the domain wall theory at low (nonzero) mass supports a 3d massless mathbb{C}{mathrm{mathbb{P}}}^{N_f-1} nonlinear σ-model with a Wess-Zumino term, in agreement with the conjectured dynamics in 2+1 dimensions.

Defect multiplets of mathcal{N}=1 supersymmetry in 4d

Any 4d theory possessing mathcal{N}=1 supersymmetry admits a so called mathcal{S} -multiplet, containing the conserved energy-momentum tensor and supercurrent. When a defect is introduced into such a theory, the mathcal{S} -multiplet receives contributions localised on the defect, which indicate the breaking of some translation symmetry and consequently also some supersymmetries. We call this the defect multiplet. We classify such terms corresponding to half-BPS defects which can be either three-dimensional, preserving 3d mathcal{N}=1 , or two-dimensional, preserving mathcal{N}=left(0,2right) . The new terms localised on the defect furnish multiplets of the reduced symmetry and give rise to the displacement operator.

Anomaly matching on the Higgs branch

We point out that we can almost always determine by the anomaly matching the full anomaly polynomial of a supersymmetric theory in 2d, 4d or 6d if we assume that its Higgs branch is the one-instanton moduli space of some group G. This method not only provides by far the simplest method to compute the central charges of known theories of this class, e.g. 4d E6,7,8 theories of Minahan and Nemeschansky or the 6d E-string theory, but also gives us new pieces of information about unknown theories of this class.

Towards deconstruction of the Type D (2,0) theory

We propose a four-dimensional supersymmetric theory that deconstructs, in a particular limit, the six-dimensional (2, 0) theory of type Dk. This 4d theory is defined by a necklace quiver with alternating gauge nodes O(2k) and Sp(k). We test this proposal by comparing the 6d half-BPS index to the Higgs branch Hilbert series of the 4d theory. In the process, we overcome several technical difficulties, such as Hilbert series calculations for non-complete intersections, and the choice of O versus SO gauge groups. Consistently, the result matches the Coulomb branch formula for the mirror theory upon reduction to 3d.

Asymptotic M5-brane entropy from S-duality

We study M5-branes compactified on S1 from the D0-D4 Witten index in the Coulomb phase. We first show that the prepotential of this index is S-dual, up to a simple anomalous part. This is an extension of the well-known S-duality of the 4d mathcal{N}=4 theory to the 6d (2, 0) theory on finite T2. Using this anomalous S-duality, we find that the asymptotic free energy scales like N3 when various temperature-like parameters are large. This shows that the number of 5d Kaluza-Klein fields for light D0-brane bound states is proportional to N3. We also compute some part of the asymptotic free energy from 6d chiral anomalies, which precisely agrees with our D0-D4 calculus.

M5-brane and D-brane scattering amplitudes

We present tree-level n-particle on-shell scattering amplitudes of various brane theories with 16 conserved supercharges. These include the world-volume theory of a probe D3-brane or D5-brane in 10D Minkowski spacetime as well as a probe M5-brane in 11D Minkowski spacetime, which describes self interactions of an abelian tensor supermultiplet with 6D (2, 0) supersymmetry. Twistor-string-like formulas are proposed for tree-level scattering amplitudes of all multiplicities for each of these theories. The R symmetry of the D3-brane theory is shown to be SU(4) × U(1), and the U(1) factor implies that its amplitudes are helicity conserving. Each of 6D theories (D5-brane and M5-brane) reduces to the D3-brane theory by dimensional reduction. As special cases of the general M5-brane amplitudes, we present compact formulas for examples involving only the self-dual B field with n = 4, 6, 8.

Nilpotent symmetries and Curci–Ferrari-type restrictions in 2D non-Abelian gauge theory: Superfield approach

We derive the off-shell nilpotent symmetries of the two [Formula: see text]-dimensional (2D) non-Abelian 1-form gauge theory by using the theoretical techniques of the geometrical superfield approach to Becchi–Rouet–Stora–Tyutin (BRST) formalism. For this purpose, we exploit the augmented version of superfield approach (AVSA) and derive theoretically useful nilpotent (anti-)BRST, (anti-)co-BRST symmetries and Curci–Ferrari (CF)-type restrictions for the self-interacting 2D non-Abelian 1-form gauge theory (where there is no interaction with matter fields). The derivation of the (anti-)co-BRST symmetries and all possible CF-type restrictions are completely novel results within the framework of AVSA to BRST formalism where the ordinary 2D non-Abelian theory is generalized onto an appropriately chosen [Formula: see text]-dimensional supermanifold. The latter is parametrized by the superspace coordinates [Formula: see text] where [Formula: see text] (with [Formula: see text]) are the bosonic coordinates and a pair of Grassmannian variables [Formula: see text] obey the relationships: [Formula: see text], [Formula: see text]. The topological nature of our 2D theory allows the existence of a tower of CF-type restrictions.

From 3d duality to 2d duality

In this paper we discuss 3d mathcal{N} = 2 supersymmetric gauge theories and their IR dualities when they are compactified on a circle of radius r, and when we take the 2d limit in which r → 0. The 2d limit depends on how the mass parameters are scaled as r → 0, and often vacua become infinitely distant in the 2d limit, leading to a direct sum of different 2d theories. For generic mass parameters, when we take the same limit on both sides of a duality, we obtain 2d dualities (between gauge theories and/or Landau-Ginzburg theories) that pass all the usual tests. However, when there are non-compact branches the discussion is subtle because the metric on the moduli space, which is not controlled by supersymmetry, plays an important role in the low-energy dynamics after compactification. Generally speaking, for IR dualities of gauge theories, we conjecture that dualities involving non-compact Higgs branches survive. On the other hand when there is a non-compact Coulomb branch on at least one side of the duality, the duality fails already when the 3d theories are compactified on a circle. Using the valid reductions we reproduce many known 2d IR dualities, giving further evidence for their validity, and we also find new 2d dualities.

Exotic matter on singular divisors in F-theory

We analyze exotic matter representations that arise on singular seven-brane configurations in F-theory. We develop a general framework for analyzing such representations, and work out explicit descriptions for models with matter in the 2-index and 3-index symmetric representations of SU(N) and SU(2) respectively, associated with double and triple point singularities in the seven-brane locus. These matter representations are associated with Weierstrass models whose discriminants vanish to high order thanks to nontrivial cancellations possible only in the presence of a non-UFD algebraic structure. This structure can be described using the normalization of the ring of intrinsic local functions on a singular divisor. We consider the connection between geometric constraints on singular curves and corresponding constraints on the low-energy spectrum of 6D theories, identifying some new examples of apparent “swampland” theories that cannot be realized in F-theory but have no apparent low-energy inconsistency.

From 6D superconformal field theories to dynamic gauged linear sigma models

Compactifications of 6D superconformal field theories (SCFTs) on four-manifolds generate a large class of novel 2d quantum field theories. We consider in detail the case of the rank one simple non-Higgsable cluster 6D SCFTs. On the tensor branch of these theories, the gauge group is simple and there are no matter fields. For compactifications on suitably chosen Kahler surfaces, we present evidence that this provides a method to realize 2d SCFTs with N = (0,2) supersymmetry. In particular, we find that reduction on the tensor branch of the 6D SCFT yields a description of the same 2d fixed point that is described in the UV by a gauged linear sigma model (GLSM) in which the parameters are promoted to dynamical fields, that is, a "dynamic GLSM" (DGLSM). Consistency of the model requires the DGLSM to be coupled to additional non-Lagrangian sectors obtained from reduction of the anti-chiral two-form of the 6D theory. These extra sectors include both chiral and anti-chiral currents, as well as spacetime filling non-critical strings of the 6D theory. For each candidate 2d SCFT, we also extract the left- and right-moving central charges in terms of data of the 6D SCFT and the compactification manifold.

Smallest 3d hyperbolic manifolds via simple 3d theories

We provide strong pieces of evidence that mathematics of three-dimensional hyperbolic manifolds of the first, second and third smallest volume are captured by the physics of three-dimensional theories composed of a complex boson and a Dirac fermion, both of a unit charge, coupled to a U(1) gauge field with the Chern-Simons levels $\ensuremath{-}5/2$, $\ensuremath{-}7/2$ and $\ensuremath{-}3/2$, respectively.

Do clinical features relate to theory of mind, empathy and 2D:4D in schizophrenia?

ABSTRACTOBJECTIVE: Digit ratios may be accepted as an indicator of level of prenatal androgen exposure during the fetal developmental period. Female-typical digit ratios have been suggested to be associated with better mentalizing and empathic abilities in general population. Recently, a number of studies have investigated the ratio of hand’s second and fourth digit fingers (2D:4D) in schizophrenia. The aim of this study was to investigate the hypothesis that positive symptoms are related to female-biased 2D:4D and relatively less impaired social cognition in schizophrenia, negative dimension is related to male-biased 2D:4D ratio and more pronounced deficits in social cognition.METHOD: The study was carried out in 48 patients with schizophrenia and 48 healthy controls. Patients were evaluated by Positive and Negative Syndrome Scale (PANSS). A digital caliper was used to measure 2D:4D finger lengths and social cognitive abilities were assessed using the Empathy Quotient (EQ) test and Reading Mind in the Ey...

Clarification and unification of the obliquity factor in diffraction and scattering theories: discussion.

Two-dimensional (2D) and three-dimensional (3D) diffraction theories form the underlying basis of quantitative phase imaging. This paper reviews how 2D and 3D diffraction theories are developed based on thin and thick object requirements. However, some previously reported work has mixed 2D and 3D theories. This discussion shows that it is possible to enable consistent mixed use of 2D and 3D theories by applying appropriate obliquity factor (OF) modifications. The discussion is concluded with an overall unifying representation for the usage of the OF modifications in 2D and 3D diffraction theories as applied to both thin and thick objects.

6D SCFTs and phases of 5D theories

Starting from 6D superconformal field theories (SCFTs) realized via F-theory, we show how reduction on a circle leads to a uniform perspective on the phase structure of the resulting 5D theories, and their possible conformal fixed points. Using the correspon-dence between F-theory reduced on a circle and M-theory on the corresponding elliptically fibered Calabi-Yau threefold, we show that each 6D SCFT with minimal supersymmetry directly reduces to a collection of between one and four 5D SCFTs. Additionally, we find that in most cases, reduction of the tensor branch of a 6D SCFT yields a 5D generalization of a quiver gauge theory. These two reductions of the theory often correspond to different phases in the 5D theory which are in general connected by a sequence of flop transitions in the extended Kähler cone of the Calabi-Yau threefold. We also elaborate on the structure of the resulting conformal fixed points, and emergent flavor symmetries, as realized by M-theory on a canonical singularity.

On exceptional instanton strings

According to a recent classification of 6d (1, 0) theories within F-theory there are only six “pure” 6d gauge theories which have a UV superconformal fixed point. The corresponding gauge groups are SU(3), SO(8), F4, E6, E7, and E8. These exceptional models have BPS strings which are also instantons for the corresponding gauge groups. For G simply-laced, we determine the 2d mathcal{N}=left(0,4right) worldsheet theories of such BPS instanton strings by a simple geometric engineering argument. These are given by a twisted S2 compactification of the 4d mathcal{N}=2 theories of type H2, D4, E6, E7 and E8 (and their higher rank generalizations), where the 6d instanton number is mapped to the rank of the corresponding 4d SCFT. This determines their anomaly polynomials and, via topological strings, establishes an interesting relation among the corresponding T2× S2 partition functions and the Hilbert series for moduli spaces of G instantons. Such relations allow to bootstrap the corresponding elliptic genera by modularity. As an example of such procedure, the elliptic genera for a single instanton string are determined. The same method also fixes the elliptic genus for case of one F4 instanton. These results unveil a rather surprising relation with the Schur index of the corresponding 4d mathcal{N}=2 models.