Dimensional Gauge Theories Research Articles

Six-dimensional regularization of chiral gauge theories

We propose a regularization of four dimensional chiral gauge theories using six-dimensional Dirac fermions. In our formulation, we consider two different mass terms having domain-wall profiles in the fifth and the sixth directions, respectively. A Weyl fermion appears as a localized mode at the junction of two different domain-walls. One domain-wall naturally exhibits the Stora-Zumino chain of the anomaly descent equations, starting from the axial U(1) anomaly in six-dimensions to the gauge anomaly in four-dimensions. Another domain-wall implies a similar inflow of the global anomalies. The anomaly free condition is equivalent to requiring that the axial U(1) anomaly and the parity anomaly are canceled among the six-dimensional Dirac fermions. Since our formulation is based on a massive vector-like fermion determinant, a non-perturbative regularization will be possible on a lattice. Putting the gauge field at the four-dimensional junction and extending it to the bulk using the Yang-Mills gradient flow, as recently proposed by Grabowska and Kaplan, we define the four-dimensional path integral of the target chiral gauge theory.

Holomorphic bundles for higher dimensional gauge theory

Motivated by gauge theory under special holonomy, we present techniques to produce holomorphic bundles over certain noncompact $3-$folds, called building blocks, satisfying a stability condition `at infinity'. Such bundles are known to parametrise solutions of the Yang-Mills equation over the $\rm G_2-$manifolds obtained from asymptotically cylindrical Calabi-Yau $3-$folds studied by Kovalev and by Corti-Haskins-Nordstr\"om-Pacini et al. The most important tool is a generalisation of Hoppe's stability criterion to holomorphic bundles over smooth projective varieties $X$ with $\operatorname{Pic}{X}\simeq\mathbb{Z}^l$, a result which may be of independent interest. Finally, we apply monads to produce a prototypical model of the curvature blow-up phenomenon along a sequence of asymptotically stable bundles degenerating into a torsion-free sheaf.

BPS/CFT correspondence II: Instantons at crossroads, moduli and compactness theorem

Gieseker-Nakajima moduli spaces $M_{k}(n)$ parametrize the charge $k$ noncommutative $U(n)$ instantons on ${\bf R}^{4}$ and framed rank $n$ torsion free sheaves $\mathcal{E}$ on ${\bf C\bf P}^{2}$ with ${\rm ch}_{2}({\mathcal{E}}) = k$. They also serve as local models of the moduli spaces of instantons on general four-manifolds. We study the generalization of gauge theory in which the four dimensional spacetime is a stratified space $X$ immersed into a Calabi-Yau fourfold $Z$. The local model ${\bf M}_{k}({\vec n})$ of the corresponding instanton moduli space is the moduli space of charge $k$ (noncommutative) instantons on origami spacetimes. There, $X$ is modelled on a union of (up to six) coordinate complex planes ${\bf C}^{2}$ intersecting in $Z$ modelled on ${\bf C}^{4}$. The instantons are shared by the collection of four dimensional gauge theories sewn along two dimensional defect surfaces and defect points. We also define several quiver versions ${\bf M}_{\bf k}^{\gamma}({\vec{\bf n}})$ of ${\bf M}_{k}({\vec n})$, motivated by the considerations of sewn gauge theories on orbifolds ${\bf C}^{4}/{\Gamma}$. The geometry of the spaces ${\bf M}_{\bf k}^{\gamma}({\vec{\bf n}})$, more specifically the compactness of the set of torus-fixed points, for various tori, underlies the non-perturbative Dyson-Schwinger identities recently found to be satisfied by the correlation functions of $qq$-characters viewed as local gauge invariant operators in the ${\mathcal{N}}=2$ quiver gauge theories. The cohomological and K-theoretic operations defined using ${\bf M}_{k}({\vec n})$ and their quiver versions as correspondences provide the geometric counterpart of the $qq$-characters, line and surface defects.

Entanglement entropy for pure gauge theories in 1+1 dimensions using the lattice regularization

We study the entanglement entropy (EE) for pure gauge theories in 1[Formula: see text]+[Formula: see text]1 dimensions with the lattice regularization. Using the definition of the EE for lattice gauge theories proposed in a previous paper,1 we calculate the EE for arbitrary pure as well as mixed states in terms of eigenstates of the transfer matrix in (1[Formula: see text]+[Formula: see text]1)-dimensional lattice gauge theory. We find that the EE of an arbitrary pure state does not depend on the lattice spacing, thus giving the EE in the continuum limit, and show that the EE for an arbitrary pure state is independent of the real (Minkowski) time evolution. We also explicitly demonstrate the dependence of EE on the gauge fixing at the boundaries between two subspaces, which was pointed out for general cases in the paper. In addition, we calculate the EE at zero as well as finite temperature by the replica method, and show that our result in the continuum limit corresponds to the result obtained before in the continuum theory, with a specific value of the counterterm, which is otherwise arbitrary in the continuum calculation. We confirm the gauge dependence of the EE also for the replica method.

Quantum entanglement of locally excited states in Maxwell theory

In 4 dimensional Maxwell gauge theory, we study the changes of (Renyi) entangle-ment entropy which are defined by subtracting the entropy for the ground state from the one for the locally excited states generated by acting with the gauge invariant local operators on the state. The changes for the operators which we consider in this paper reflect the electric-magnetic duality. The late-time value of changes can be interpreted in terms of electromagnetic quasi-particles. When the operator constructed of both electric and magnetic fields acts on the ground state, it shows that the operator acts on the late-time structure of quantum entanglement differently from free scalar fields.

Physical effects of the gravitational Θ-parameter

We describe the effect of the gravitational [Formula: see text]-parameter on the behavior of the stretched horizon of a black hole in [Formula: see text]-dimensions. The gravitational [Formula: see text]-term is a total derivative, however, it affects the transport properties of the horizon. In particular, the horizon acquires a third-order parity violating, dimensionless transport coefficient which affects the way localized perturbations scramble on the horizon. In the context of the gauge/gravity duality, the [Formula: see text]-term induces a nontrivial contact term in the energy–momentum tensor of a [Formula: see text]-dimensional large-N gauge theory, which admits a dual gravity description. As a consequence, the dual gauge theory in the presence of the [Formula: see text]-term acquires the same third-order parity violating transport coefficient.

A magnetically induced quantum critical point in holography

We investigate quantum phase transitions in a 2+1 dimensional gauge theory at finite chemical potential $\chi$ and magnetic field $B$. The gravity dual is based on 4D $\mathcal{N}=2$ Fayet-Iliopoulos gauged supergravity and the solutions we consider---that are constructed analytically---are extremal, dyonic, asymptotically $AdS_4$ black-branes with a nontrivial radial profile for the scalar field. We discover a line of second order fixed points at $B=B_c(\chi)$ between the dyonic black brane and an extremal "thermal gas" solution with a singularity of good-type, according to the acceptability criteria of Gubser [1]. The dual field theory is the ABJM theory [2] deformed by a triple trace operator $\Phi^3$ and placed at finite charge and magnetic field. This line of fixed points might be useful in studying the various strongly interacting quantum critical phenomena such as the ones proposed to underlie the cuprate superconductors. We also find curious similarities between the behaviour of the VeV $\langle \Phi \rangle$ under B and that of the quark condensate in 2+1 dimensional NJL models.

3d deconfinement, product gauge group, Seiberg-Witten and new 3d dualities

We construct a three dimensional deconfinement method which enables us to find new three-dimensional dualities and we apply various techniques developed in four dimensional supersymmetric gauge theories, such as the product gauge groups and Seiberg-Witten curves to the three dimensional $\mathcal{N}=2$ supersymmetric gauge theories. Dual descriptions of three dimensional $\mathcal{N}=2$ supersymmetric gauge theories which involve two-index matters, for example, adjoint, symmetric, and anti-symmetric matters without superpotentials can be obtained. These matters are described in terms of s-confining phases of the supersymmetric gauge theories.

A Lie based 4–dimensional higher Chern–Simons theory

We present and study a model of 4–dimensional higher Chern-Simons theory, special Chern–Simons (SCS) theory, instances of which have appeared in the string literature, whose symmetry is encoded in a skeletal semistrict Lie 2–algebra constructed from a compact Lie group with non discrete center. The field content of SCS theory consists of a Lie valued 2–connection coupled to a background closed 3–form. SCS theory enjoys a large gauge and gauge for gauge symmetry organized in an infinite dimensional strict Lie 2–group. The partition function of SCS theory is simply related to that of a topological gauge theory localizing on flat connections with degree 3 second characteristic class determined by the background 3–form. Finally, SCS theory is related to a 3–dimensional special gauge theory whose 2–connection space has a natural symplectic structure with respect to which the 1–gauge transformation action is Hamiltonian, the 2–curvature map acting as moment map.

M2-brane surface operators and gauge theory dualities in Toda

We give a microscopic two dimensional ${\cal N}=(2,2)$ gauge theory description of arbitrary M2-branes ending on $N_f$ M5-branes wrapping a punctured Riemann surface. These realize surface operators in four dimensional ${\cal N}=2$ field theories. We show that the expectation value of these surface operators on the sphere is captured by a Toda CFT correlation function in the presence of an additional degenerate vertex operator labelled by a representation ${\cal R}$ of $SU(N_f)$, which also labels M2-branes ending on M5-branes. We prove that symmetries of Toda CFT correlators provide a geometric realization of dualities between two dimensional gauge theories, including ${\cal N}=(2,2)$ analogues of Seiberg and Kutasov--Schwimmer dualities. As a bonus, we find new explicit conformal blocks, braiding matrices, and fusion rules in Toda CFT.

Elliptic CY3folds and non-perturbative modular transformation

We study the refined topological string partition function of a class of toric elliptically fibered Calabi-Yau threefolds. These Calabi-Yau threefolds give rise to five dimensional quiver gauge theories and are dual to configurations of M5-M2-branes. We determine the Gopakumar-Vafa invariants for these threefolds and show that the genus $g$ free energy is given by the weight $2g$ Eisenstein series. We also show that although the free energy at all genera are modular invariant the full partition function satisfies the non-perturbative modular transformation property discussed by Lockhart and Vafa in arXiv:1210.5909 and therefore the modularity of free energy is up to non-perturbative corrections.

Basic Brackets of a 2D Model for the Hodge Theory Without its Canonical Conjugate Momenta

We deduce the canonical brackets for a two (1 + 1)-dimensional (2D) free Abelian 1-form gauge theory by exploiting the beauty and strength of the continuous symmetries of a Becchi-Rouet-Stora-Tyutin (BRST) invariant Lagrangian density that respects, in totality, six continuous symmetries. These symmetries entail upon this model to become a field theoretic example of Hodge theory. Taken together, these symmetries enforce the existence of exactly the same canonical brackets amongst the creation and annihilation operators that are found to exist within the standard canonical quantization scheme. These creation and annihilation operators appear in the normal mode expansion of the basic fields of this theory. In other words, we provide an alternative to the canonical method of quantization for our present model of Hodge theory where the continuous internal symmetries play a decisive role. We conjecture that our method of quantization is valid for a class of field theories that are tractable physical examples for the Hodge theory. This statement is true in any arbitrary dimension of spacetime.

Double-soft behavior for scalars and gluons from string theory

We compute the leading double-soft behavior for gluons and for the scalars obtained by dimensional reduction of a higher dimensional pure gauge theory, from the scattering amplitudes of gluons and scalars living in the world-volume of a Dp-brane of the bosonic string. In the case of gluons, we compute both the double-soft behavior when the two soft gluons are contiguous as well as when they are not contiguous. From our results, that are valid in string theory, one can easily get the double-soft limit in gauge field theory by sending the string tension to infinity.

On the reduction of 4d N = 1 $$ \mathcal{N}=1 $$ theories on S 2 $$ {\mathbb{S}}^2 $$

We discuss reductions of general N=1 four dimensional gauge theories on S^2. The effective two dimensional theory one obtains depends on the details of the coupling of the theory to background fields, which can be translated to a choice of R-symmetry. We argue that, for special choices of R-symmetry, the resulting two dimensional theory has a natural interpretation as an N=(0,2) gauge theory. As an application of our general observations, we discuss reductions of N=1 and N=2 dualities and argue that they imply certain two dimensional dualities.

Twisted gauge theory model of topological phases in three dimensions

We propose an exactly solvable lattice Hamiltonian model of topological phases in $3+1$ dimensions, based on a generic finite group $G$ and a $4$-cocycle $\omega$ over $G$. We show that our model has topologically protected degenerate ground states and obtain the formula of its ground state degeneracy on the $3$-torus. In particular, the ground state spectrum implies the existence of purely three-dimensional looplike quasi-excitations specified by two nontrivial flux indices and one charge index. We also construct other nontrivial topological observables of the model, namely the $SL(3,\mathbb{Z})$ generators as the modular $S$ and $T$ matrices of the ground states, which yield a set of topological quantum numbers classified by $\omega$ and quantities derived from $\omega$. Our model fulfills a Hamiltonian extension of the $3+1$-dimensional Dijkgraaf-Witten topological gauge theory with a gauge group $G$. This work is presented to be accessible for a wide range of physicists and mathematicians.

Thermal fluctuations and meson melting: a holographic approach

We use gauge/gravity duality to investigate the effect of thermal fluctuations on the dissociation of the quarkonium mesons in strongly coupled (3+1)-dimensional gauge theories. The purpose of this paper is to introduce a new approach to study the instability and probable first-order phase transition of a probe D7-brane in the dual gravity theory. We explicitly show that for the Minkowski embeddings with their tips close to the horizon in the background, the long wavelength thermal fluctuations lead to an imaginary term in their action, signaling an instability in the system. Due to this instability, a phase transition is expected. On the gauge theory side, it indicates that the quarkonium mesons are not stable and dissociate in the plasma. Identifying the imaginary part of the probe brane action with the thermal width of the mesons, we observe that the thermal width increases as one decreases the mass of the quarks. Also keeping the mass fixed, thermal width increases by temperature as expected. We will also investigate the effect of the magnetic field on the mass and the thermal width.

Defects and quantum Seiberg-Witten geometry

We study the Nekrasov partition function of the five dimensional U(N) gauge theory with maximal supersymmetry on R^4 x S^1 in the presence of codimension two defects. The codimension two defects can be described either as monodromy defects, or by coupling to a certain class of three dimensional quiver gauge theories on R^2 x S^1. We explain how these computations are connected with both classical and quantum integrable systems. We check, as an expansion in the instanton number, that the aforementioned partition functions are eigenfunctions of an elliptic integrable many-body system, which quantizes the Seiberg-Witten geometry of the five-dimensional gauge theory.

Flux and Hall states in ABJM with dynamical flavors

We study the physics of probe D6-branes with quantized internal worldvolume flux in the ABJM background with unquenched massless flavors. This flux breaks parity in the (2+1)-dimensional gauge theory and allows quantum Hall states. Parity breaking is also explicitly demonstrated via the helicity dependence of the meson spectrum. We obtain general expressions for the conductivities, both in the gapped Minkowski embeddings and in the compressible black hole ones. These conductivities depend on the flux and contain a contribution from the dynamical flavors which can be regarded as an effect of intrinsic disorder due to quantum fluctuations of the fundamentals. We present an explicit, analytic family of supersymmetric solutions with nonzero charge density, electric, and magnetic fields.

Deconstruction, holography and emergent supersymmetry

We study a gauge theory in a 5D warped space via the dimensional deconstruction that a higher dimensional gauge theory is constructed from a moose of 4D gauge groups. By the AdS/CFT correspondence, a 5D warped gauge theory is dual to a 4D conformal field theory (CFT) with a global symmetry. As far as physics of the gauge theory, we obtain the one-to-one correspondence between each component of a moose of gauge groups and that of a CFT. We formulate a supersymmetric extension of deconstruction and explore the framework of natural supersymmetry in a 5D warped space — the super-symmetric Randall-Sundrum model with the IR-brane localized Higgs and bulk fermions — via the gauge moose. In this model, a supersymmetry breaking source is located at the end of the moose corresponding to the UV brane and the first two generations of squarks are decoupled. With left-right gauge symmetries in the bulk of the moose, we demonstrate realization of accidental or emergent supersymmetry of the Higgs sector in comparison with the proposed “Moose/CFT correspondence.”

Wilson Loops with Arbitrary Charges

We discuss how to implement, in lattice gauge theories, external charges which are not commensurate with an elementary gauge coupling. It is shown that an arbitrary, real power of a standard Wilson loop (or Polyakov line) can be defined and consistently computed in lattice formulation of non-abelian, two dimensional gauge theories. However, such an observable can excite quantum states with integer fluxes only. Since the non-integer fluxes are not in the spectrum of the theory they cannot be created, no matter which observable is chosen. Also the continuum limit of above averages does not exist unless the powers in question are in fact integer. On the other hand, a new continuum limit exists, which is rather intuitive, and where above observables make perfect sense and lead to the string tension proportional to the square of arbitrary (non necessary commensurate with gauge coupling) charge.