Flux String Research Articles

Electroweak strings in the standard model

We argue that the existence of the electroweak monopole predicts the existence of the electroweak string in the standard model made of monopole–antimonopole pair separated infinitely apart, which carry the quantized magnetic flux 4πn/e\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4 \\pi n/e$$\\end{document}. We show how to construct such quantized magnetic flux string solution. Our result strongly indicates that genuine fundamental electromagnetic string could exist in nature which could actually be detected. We discuss the physical implications of our result in cosmology.

Bounds on field range for slowly varying positive potentials

In the context of quantum gravitational systems, we place bounds on regions in field space with slowly varying positive potentials. Using the fact that V<Λs2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ V<{\\Lambda}_s^2 $$\\end{document}, where Λs(ϕ) is the species scale, and the emergent string conjecture, we show this places a bound on the maximum diameter of such regions in field space: ∆ϕ ≤ a log(1/V) + b in Planck units, where a ≤ d−1d−2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{\\left(d-1\\right)\\left(d-2\\right)} $$\\end{document}, and b is an \U0001d4aa(1) number and expected to be negative. The coefficient of the logarithmic term has previously been derived using TCC, providing further confirmation. For type II string flux compactifications on Calabi-Yau threefolds, using the recent results on the moduli dependence of the species scale, we can check the above relation and determine the constant b, which we verify is \U0001d4aa(1) and negative in all the examples we studied.

Magnetic flux in the vacuum of quantum bosonic matter in the cosmic string background

The relativistic spin-0 matter field is quantized in the background of a straight cosmic string with nonvanishing transverse size. The most general boundary condition ensuring the impenetrability of the matter field into the interior of the cosmic string is shown to be the Robin condition with a boundary parameter varying arbitrarily from point to point of the boundary. The role of the bound states in the spectrum of solutions to the Fock-Klein-Gordon equation is elucidated. We derive, in the general case, an analytic expression for the total magnetic flux which is induced in the vacuum in the cosmic string background. The further numerical analysis and requirement of physical plausibility are shown to restrict ambiguity which is due to the boundary condition. The dependence of the induced vacuum magnetic flux on the string flux and tension, as well as on the transverse size of the string, is analyzed.

Spin gauge theory, duality and fermion pairing

We apply duality transformation to the Abelian Higgs model in 3+1 dimensions in the presence of electrons coupled to the gauge field. The Higgs field is in the symmetry broken phase, where flux strings can form. Dualization brings in an antisymmetric tensor potential Bμν, which couples to the electrons through a nonlocal interaction which can be interpreted as a coupling to the spin current. It also couples to the string worldsheet and gives rise to a string Higgs mechanism via the condensation of flux strings. In the phase where the Bμν field is massless, the nonlocal interaction implies a linearly rising attractive force between the electrons, which can be interpreted as the result of a pair of strings joining the electrons.

Induced vacuum magnetic field in the cosmic string background

The relativistic charged spinor matter field is quantized in the background of a straight cosmic string with nonvanishing transverse size. The most general boundary conditions ensuring the impossibility for matter to penetrate through the edge of the string core are considered. The role of discrete symmetries is elucidated, and analytic expressions for the temporal and spatial components of the induced vacuum current are derived in the case of either $P$ or $CT$ invariant boundary condition with two parameters varying arbitrarily from point to point of the edge. The requirement of physical plausibility for the global induced vacuum characteristics is shown to remove completely an arbitrariness in boundary conditions. We find out that a magnetic field is induced in the vacuum and that a sheath in the form of a tube of the magnetic flux lines encloses a cosmic string. The dependence of the induced vacuum magnetic field strength on the string flux and tension, as well as on the transverse size of the string and on the distance from the string, is unambiguously determined.

Flux tubes and string breaking in three dimensional SU(2) Yang-Mills theory

We consider the three dimensional SU(2) Yang-Mills theory with adjoint static color sources, studying by lattice simulations how the shape of the flux tube changes when increasing the distance between them. The disappearance of the flux tube at string breaking is quite abrupt, but precursors of this phenomenon are present already when the separation between the sources is smaller than its critical value, a fact that influences also some details of the static potential.

Fat inflatons, large turns and the η-problem

It is commonly believed that a successful period of inflation driven by a single or several scalar fields requires a specific hierarchy of masses given by Minf≪ H ≪ Mheavy, where Minf can correspond to several or a single light field and Mheavy corresponds to any heavy field that might be integrated out if it satisfies suitable conditions. This is at the heart of the so called η-problem in inflation, since large contributions to the masses of the inflatons might spoil the slow-roll conditions required for inflation. We show that, while this is an unavoidable conclusion in single field inflation, in multifield inflation, heavy fields as defined above, may be fully responsible for a successful period of what we call fat slow-roll inflation. Moreover we show that in this scenario, the turning rate of the inflationary trajectory, Ω/H, is larger than one. Thus, the η-problem is evaded with large turns in fat inflation. Depending on the perturbations' mass spectra, cosmological predictions will differ either slightly or largely with respect to those of the single field case. We illustrate this scenario in a concrete example in Type IIB string flux compactifications, where a probe D5-brane moving along the angular and radial directions in a warped throat drives fat D5-brane natural inflation. An instantaneous superplanckian decay constant can be defined, consistent with our low energy approximations. We compute the cosmological observables, which are consistent with Planck data, ameliorating the tension of single field natural inflation with observations. We also discuss fat inflation in the context of recently proposed swampland de Sitter conjectures.

How many fluxes fit in an EFT?

We extend the recent construction of 4d mathcal{N}=1 three-form Lagrangians by including the most general three-form multiplets necessary to reproduce any F-term potential in string flux compactifications. In this context we find an obstruction to dualize all fluxes to three-forms in the effective field theory. This implies that, generically, a single EFT cannot capture all the membrane-mediated flux transitions expected from a string theory construction, but only a sublattice of them. The obstruction can be detected from the maximal number of three-forms per scalar in any supermultiplet, and from the gaugings involving three-forms that appear in the EFT. Some gaugings are related to the appearance of fluxes in the tadpole conditions, and give a general obstruction. Others are related to the anomalous axionic strings present in a specific compactification regime. We illustrate the structure of the three-form Lagrangian in type II and F/M-theory setups, where we argue that the above obstructions correlate with the different 4d membrane tensions with respect to the EFT energy scales.

Three-forms, dualities and membranes in four-dimensional supergravity

We consider four-dimensional mathcal{N}=1 supergravity models of a kind appearing in string flux compactifications. It has been recently shown that, by using double three-form multiplets instead of ordinary chiral multiplets, one can promote to dynamical variables (part of) the quantized numbers appearing in the flux-induced superpotential. We show that double three-form multiplets naturally transform under symplectic dualities associated with the special Kähler structure that characterizes their scalar sector. Furthermore, we discuss how to couple membranes which carry arbitrary ‘electric-magnetic’ charges. The complete action is supersymmetric, kappa-symmetric and duality covariant. As an application, we derive the flow equations for BPS domain walls sourced by membranes and give simple analytic examples of their solution.

From the SU(2) quantum link model on the honeycomb lattice to the quantum dimer model on the kagome lattice: Phase transition and fractionalized flux strings

We consider the $(2+1)$-d $SU(2)$ quantum link model on the honeycomb lattice and show that it is equivalent to a quantum dimer model on the Kagom\'e lattice. The model has crystalline confined phases with spontaneously broken translation invariance associated with pinwheel order, which is investigated with either a Metropolis or an efficient cluster algorithm. External half-integer non-Abelian charges (which transform non-trivially under the $\mathbb{Z}(2)$ center of the $SU(2)$ gauge group) are confined to each other by fractionalized strings with a delocalized $\mathbb{Z}(2)$ flux. The strands of the fractionalized flux strings are domain walls that separate distinct pinwheel phases. A second-order phase transition in the 3-d Ising universality class separates two confining phases; one with correlated pinwheel orientations, and the other with uncorrelated pinwheel orientations.

A megaxion at 750 GeV as a first hint of low scale string theory

Low scale string models naturally have axion-like pseudoscalars which couple directly to gluons and photons (but not $W$s) at tree level. We show how they typically get tree level masses in the presence of closed string fluxes, consistent with the axion discrete gauge symmetry, in a way akin of the axion monodromy of string inflation and relaxion models. We discuss the possibility that the hints for a resonance at 750 GeV recently reported at ATLAS and CMS could correspond to such a heavy axion state (megaxion). Adjusting the production rate and branching ratios suggests the string scale to be of order $M_s$ ~ $7 - 10^4$ TeV, depending on the compactification geometry. If this interpretation was correct, one extra $Z'$ gauge boson could be produced before reaching the string threshold at LHC and future colliders.

Canonical transformations and loop formulation of SU(N) lattice gauge theories

We construct canonical transformations to reformulate SU(N) Kogut-Susskind lattice gauge theory in terms of a set of fundamental loop & string flux operators along with their canonically conjugate loop & string electric fields. We show that as a consequence of SU(N) Gauss laws all SU(N) string degrees of freedom become cyclic and decouple from the physical Hilbert space ${\cal H}^p$. The canonical relations between the initial SU(N) link operators and the final SU(N) loop & string operators over the entire lattice are worked out in a self consistent manner. The Kogut-Susskind Hamiltonian rewritten in terms of the fundamental physical loop operators has global SU(N) invariance. There are no gauge fields. We further show that the $(1/g^2)$ magnetic field terms on plaquettes create and annihilate the fundamental plaquette loop fluxes while the $(g^2)$ electric field terms describe all their interactions. In the weak coupling ($g^2 \rightarrow 0$) continuum limit the SU(N) loop dynamics is described by SU(N) spin Hamiltonian with nearest neighbour interactions. In the simplest SU(2) case, where the canonical transformations map the SU(2) loop Hilbert space into the Hilbert spaces of hydrogen atoms, we analyze the special role of the hydrogen atom dynamical symmetry group $SO(4,2)$ in the loop dynamics and the spectrum. A simple tensor network ansatz in the SU(2) gauge invariant hydrogen atom loop basis is discussed.

Minkowski 3-forms, flux string vacua, axion stability and naturalness

We discuss the role of Minkowski 3-forms in flux string vacua. In these vacua all internal closed string fluxes are in one to one correspondence with quantized Minkowski 4-forms. By performing a dimensional reduction of the $D=10$ Type II supergravity actions we find that the 4-forms act as auxiliary fields of the Kahler and complex structure moduli in the effective action. We show that all the RR and NS axion dependence of the flux scalar potential appears through the said 4-forms. Gauge invariance of these forms then severely restricts the structure of the axion scalar potentials. Combined with duality symmetries it suggests that all perturbative corrections to the leading axion scalar potential $V_0$ should appear as an expansion in powers of $V_0$ itself. These facts could have an important effect e.g. on the inflaton models based on F-term axion monodromy. We also suggest that the involved multi-branched structure of string vacua provides for a new way to maintain interacting scalar masses stable against perturbative corrections.

MAP, MAC, and vortex-rings configurations in the Weinberg–Salam model

We report on the presence of new axially symmetric monopoles, antimonopoles and vortex-rings solutions of the SU(2)×U(1) Weinberg–Salam model of electromagnetic and weak interactions. When the ϕ-winding number n=1, and 2, the configurations are monopole–antimonopole pair (MAP) and monopole–antimonopole chain (MAC) with poles of alternating sign magnetic charge arranged along the z-axis. Vortex-rings start to appear from the MAP and MAC configurations when the winding number n=3. The MAP configurations possess zero net magnetic charge whereas the MAC configurations possess net magnetic charge of 4πn/e.In the MAP configurations, the monopole–antimonopole pair is bounded by the Z0 field flux string and there is an electromagnetic current loop encircling it. The monopole and antimonopole possess magnetic charges ±4πnesin2θW respectively. In the MAC configurations there is no string connecting the monopole and the adjacent antimonopole and they possess magnetic charges ±4πne respectively. The MAC configurations possess infinite total energy and zero magnetic dipole moment whereas the MAP configurations which are actually sphalerons possess finite total energy and magnetic dipole moment. The configurations were investigated for varying values of Higgs self-coupling constant 0≤λ≤40 at Weinberg angle θW=π4.

Non-Abelian string breaking phenomena with matrix product states

Using matrix product states, we explore numerically the phenomenology of string breaking in a non-Abelian lattice gauge theory, namely 1+1 dimensional SU(2). The technique allows us to study the static potential between external heavy charges, as traditionally explored by Monte Carlo simulations, but also to simulate the real-time dynamics of both static and dynamical fermions, as the latter are fully included in the formalism. We propose a number of observables that are sensitive to the presence or breaking of the flux string, and use them to detect and characterize the phenomenon in each of these setups.

String flux mechanism for fractionalization in topologically ordered phases

We construct a family of exactly solvable spin models that illustrate a novel mechanism for fractionalization in topologically ordered phases, dubbed the string flux mechanism. The essential idea is that an anyon of a topological phase can be endowed with fractional quantum numbers when the string attached to it slides over a background pattern of flux in the ground state. The string flux models that illustrate this mechanism are $Z_n$ quantum double models defined on specially constructed $d$-dimensional lattices, and possess $Z_n$ topological order for $d \geq 2$. The models have a unitary, internal symmetry $G$, where $G$ is an arbitrary finite group. The simplest string flux model is a $Z_2$ toric code defined on a bilayer square lattice, where $G = Z_2$ is layer-exchange symmetry. In general, by varying the pattern of $Z_n$ flux in the ground state, any desired fractionalization class [element of $H^2(G, Z_n)$] can be realized for the $Z_n$ charge excitations. While the string flux models are not gauge theories, they map to $Z_n$ gauge theories in a certain limit, where they follow a novel magnetic route for the emergence of low-energy gauge structure. The models are analyzed by studying the action of $G$ symmetry on $Z_n$ charge excitations, and by gauging the $G$ symmetry. The latter analysis confirms that distinct fractionalization classes give rise to distinct quantum phases, except that classes $[\omega], [\omega]^{-1} \in H^2(G, Z_n)$ give rise to the same phase. We conclude with a discussion of open issues and future directions.

Deconfinement transition as black hole formation by the condensation of QCD strings

We argue that the deconfinement transition of large-$N$ Yang-Mills theory is the condensation of very long and self-intersecting chromo-electric flux strings (QCD string), which is analogous to the formation of a black hole in string theory. We do this by using lattice gauge theory and matrix models. As evidence, we derive an analytic formula for the deconfinement temperature in the strong coupling limit and confirm it numerically. Dual gravity descriptions interpreted in this manner should make it possible to understand the details of the formation of black holes in terms of fundamental strings. We argue that very simple matrix models capture the essence of the formation of black holes.

Two-dimensional lattice gauge theories with superconducting quantum circuits

A quantum simulator of U(1) lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models. Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well. Here we show how state-of-the-art superconducting technology allows us to simulate these phenomena in relatively small circuit lattices. By exploiting the strong non-linear couplings between quantized excitations emerging when superconducting qubits are coupled, we show how to engineer gauge invariant Hamiltonians, including ring-exchange and four-body Ising interactions. We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories. The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability.

Coolant Flow Estimation in Natural Circulation BWR

This work presents the design and implementation of an advanced controller in real time for the estimation of coolant flows through fuel assemblies about standard neutron flux strings of a boiling water reactor (BWR) reactor core cooled by natural circulating water. During all operations of a natural circulating BWR, the fuel assembly's coolant flow is one of the main variables to consider. The goal of this advanced controller is to reduce penalties associated with operation limits established due to coolant flow uncertainties. The design of the controller was based on the theory of an extended Kalman filter. The estimator flow uses the equivalent electrical model, which was developed from the analogies between electrical current and voltage with coolant flows and pressure drops. Results obtained from computer simulations indicate that the best estimations of the total core flow are possible for the natural circulating BWR.

Flux-induced soft terms on type IIB/F-theory matter curves and hypercharge dependent scalar masses

Closed string fluxes induce generically SUSY-breaking soft terms on supersymmetric type IIB orientifold compactifications with D3/D7 branes. This was studied in the past by inserting those fluxes on the DBI+CS actions for adjoint D3/D7 fields, where D7-branes had no magnetic fluxes. In the present work we generalise those computations to the phenomenologically more relevant case of chiral bi-fundamental fields laying at 7-brane intersections and F-theory local matter curves. We also include the effect of 7-brane magnetic flux as well as more general closed string backgrounds, including the effect of distant (anti-)D3-branes. We discuss several applications of our results. We find that squark/slepton masses become in general flux-dependent in F-theory GUT's. Hypercharge-dependent non-universal scalar masses with a characteristic sfermion hierarchy m_E^2 < m_L^2 < m_Q^2 < m_D^2 < m_U^2 are obtained. There are also flavor-violating soft terms both for matter fields living at intersecting 7-branes or on D3-branes at singularities. They point at a very heavy sfermion spectrum to avoid FCNC constraints. We also discuss the possible microscopic description of the fine-tuning of the EW Higgs boson in compactifications with a MSSM spectrum.