# Topological Solitons, Nonperturbative Gauge Dynamics and Confinement

20-21 July 2017
Department of Physics, University of Pisa
Europe/Rome timezone

## Talks & Abstracts

LIST OF TALKS & ABSTRACTS

Roberto Auzzi (Universita’ Cattolica di Brescia)

Title: On Newton-Cartan trace anomalies

Abstract: Ill discuss trace anomalies for non-relativistic Schroedinger theories in 2+1 dimensions coupled to a Newton-Cartan gravity background, which is used as a source fo the energy-momentum tensor.  The motivation is to identify candidates for a possible non-relativistic version of the a-theorem for theories with RG flows interpolating between an UV and an IR Schroedinger-invariant non-relativistic conformal fixed points.  Ill first discuss the general structure of the anomaly, which is determined by Wess-Zumino consistency condition. Then I`ll present an explicit calculation for the anomaly in the case of a free scalar and of a free fermion, using heat kernel. There is a type A anomaly which is proportional to 1/m, where m is the mass of the particle.  In analogy with the relativistic case, the irreversibility properties of the renormalization group can also be investigated by studying the Wess-Zumino consistency conditions for the trace anomaly of the theory in a Newton Cartan background with space-time dependent couplings.

Francesco Bigazzi (INFN Firenze)

Title: Theta dependence in holographic QCD

Abstract: Using the holographic gauge/gravity duality as a tool, I will consider the effects of the CP-breaking topological theta term in the large N QCD-like model by Witten, Sakai and Sugimoto. I will first focus on the ground state energy density, the topological susceptibility and the masses of the lowest lying mesons, showing agreement with expectations from the chiral effective action. Then I will consider the baryonic sector in the case with two degenerate light quarks. I will show that while the baryon spectrum does not receive corrections to first order in theta, this is not the case for observables like the electromagnetic form factor of the nucleons. In particular, it exhibits a dipole term, which turns out to be vector-meson dominated. The resulting neutron electric dipole moment, which is exactly the opposite as that of the proton, is of the same order of magnitude of previous estimates in the literature.
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Marco Bochicchio (INFN Roma)

Title: Renormalization, open/closed string duality, and twistor strings in large­-N QCD­-like theories

Abstract: Recently, we showed in Phys. Rev. D 95, 054010 that in the large­-N ’t Hooft expansion the Yang­-Mills (YM) S matrix is ultraviolet (UV) finite, while the QCD S matrix is only renormalizable due to meson-­loop log divergences. The UV finiteness of the large­-N YM S matrix is compatible with the universally believed UV finiteness of closed­-string diagrams, but open/closed duality turns out to be incompatible with the UV divergence of glueball amplitudes with the insertion of meson loops in large­-N QCD. The inconsistency arises in the would-­be canonical string solution because such UV­-divergent open­-string loop amplitudes are dual to tree closed­-string diagrams which are universally believed to be both UV finite since they are closed­-string tree diagrams and infrared finite because of the glueball mass gap. Therefore, the long sought­-after canonical string solution of large­-N QCD does not actually exist. In certain noncommutative twistor string theories the inconsistency is naturally avoided: the one-­loop space­time effective action, which arises on the fiber of the twistor fibration, gets noncanonical contributions from string instantons wrapping planar Riemann surfaces with any number of holes, in such a way that the open/closed duality is spoiled for the space­time effective action. On the base of the twistor fibration the string instantons occur as magnetic vortices in space­time.

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Ugo Bruzzo (SISSA Trieste)

Title: Instantons on stacky ALE spaces

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Andrea Cappelli (Universita' di Firenze)

Title: Three-dimensional topological insulators and bosonization

Abstract: Massless excitations at the edge of topological insulators possess both fermionic and bosonic descriptions. In two dimensions, the map between bosons and fermions is well understood within the edge conformal field theory. In three dimensions, we use effective actions and partition functions to establish some basic properties of the corresponding bosonization map.

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Chandrasekhar Chatterjee (Keio University, Japan)

Title: BPS Alice strings

Abstract: When a charged particle encircles around an Alice string, it changes the sign of the electric charge. We discuss a BPS-saturated Alice string in U(1) × SO(3) gauge theory with charged complex scalar fields belonging to the vector representation. After performing BPS completion we solve the BPS equations numerically. We discuss zero modes of a single Alice string and construct the effective action. We further embed the Alice string into an N = 1 supersymmetric gauge theory to show that it is half BPS.

Massimo D'Elia (Universita' di Pisa)

Title: Theta dependence in QCD

Abstract: I will review some recent results regarding the dependence of the vacuum energy and of the free energy of QCD and QCD-like theories on the topological angle theta, with a particular focus on the differences between the confined and the deconfined phase and on the implications for the QCD axion.

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Adriano Di Giacomo (Universita' di Pisa)

Title: Defining an order parameter for monopole condensation in QCD

Abstract: The problems encountered in defining an order parameter for confinement in lattice QCD are discussed together with their solution.

Daniele Dorigoni (Durham University, UK)

Title: New solitons solutions in eta-deformed PCM

Abstract: In this talk we discuss the SU(2) Principal Chiral Model (PCM) in the presence of an integrable η-deformation. We review some basic concept in resurgence theory and, by studying the large order behaviour of perturbation theory, we recover new non-perturbative effects called fractons, responsible for the IR renormalons. We show that these fractons are modified from the standard PCM due to the presence of this η-deformation but they are still the constituents of uniton-like solitons in a complexification of the deformed quantum field theory.

Minoru Eto (Yamagata University, Japan)

Title: Geometric Higgs Mechanism and Soliton World Scenario

Abstract: We first present a field theoretical model unifying GUT and brane world scenario in non­compact extra dimensions by using topological solitons. As a concrete example, we consider SU(5) GUT in 4+1 dimensional Minkowski spacetime. A field­dependent gauge kinetic term is used to localize massless non­Abelian gauge fields on the domain walls and to assure the charge universality of matter fields. We find the domain walls with the symmetry breaking SU(5) to SU(3)xSU(2)xU(1), which we call the geometric Higgs mechanism, as a global minimum and all the undesirable moduli are stabilized with the GUT scale. Profiles of massless Standard Model particles are determined at the same time. The proton decay can be exponentially suppressed. Secondly, we consider higher dimensional extension and address how more realistic SM physics can automatically appear on the topological solitons.

Jarah Evslin (IMP Lanzhou, China)

Title: Spiked Monopole Scattering

Nando Gliozzi (Universita' di Torino)

Title: Anomalous dimensions without Feynman diagrams

Abstract: The mechanism of conformal multiplet recombination set up by null states of CFTs in diverse dimensions allows to compute, to the first non trivial order in the epsilon expansion, the anomalous dimensions and the OPE coefficients of infinite classes of local operators, using just the CFT data of the nearby free theory.

Simone Giacomelli (ICTP Trieste)

Title: Compactification of dualities with decoupled operators and 3d mirror symmetry

Abstract: We consider supersymmetric theories with operators below the unitarity bound. In order to embed the information of the decoupling of these operators, we reformulate the theories adding gauge-singlet fields. In this way it's possible to compute chiral rings and dimensionally reduce dualities involving decoupled operators. We illustrate the usefulness of our method in a class of dualities between certain SU(N) gauge theories and Argyres-Douglas models recently found by Maruyoshi and Song. We reduce the duality to three dimensions, showing that A_{2N-1} Argyres-Douglas theory becomes N=4 SQED with N flavors. We check our claims at the level of chiral rings, sphere partition functions and mirror dual RG flows. Crucial in our analysis is a concept of chiral ring stability, which dinamically modifies the superpotential and allows for accidental symmetries.

Gianluca Grignani (Universita' di Perugia)

Title: Force free electrodynamics approach to black hole magnetosphere

Abstract: The static monopole is a solution of the force free electrodynamics (FFE) equations in a Schwarzschild metric background. To obtain a solution in a Kerr background, a perturbation theory for small black hole angular momentum was first considered and this led to the celebrated Blandford and Znajek solution as the first perturbative correction to the static monopole. We show that the perturbation theory around the static monopole is actually inconsistent and we propose to perturb around the rotating monopole solution, this might lead to a new, everywhere well defined, solution of the FFE equations in a Kerr black hole.

Title: Vortex line formation in He II

Abstract: For helium II inside a rotating cylinder, it is proposed that the formation of vortex lines of the frictionless superfluid component of the liquid is caused by the presence of the rotating quasi-particles gas.  By minimising the free energy of the system, the critical value Omega_0 of the angular velocity for the formation of the first vortex line is determined.

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Sven Bjarke Gudnason (IMP Lanzhou, China)

Title: Some exact Bradlow vortex solutions

Abstract: I will discuss Manton's five vortex equations, the action giving rise the generic equation and a different toy model giving rise to the Bradlow equation. The integrable cases have a geometric interpretation and are related to the vortex map (squared) being a ratio of the Baptista metric to the background metric. Both metrics give rise to constant Gaussian curvatures, except at the vortex positions where the Baptista metric has conical singularities with a conical excess of 2pi per vortex. The Gaussian curvature of the background metric is given by the (Fayet­Iliopoulos) constant in the vortex equation and the Gaussian curvature of the Baptista metric is given by the constant multiplying the scalar field (squared). All the known integrable cases have constant background curvature. For the Bradlow vortex, it is not necessary, though, due to the simplicity of the equation. I present some simple solutions with non­constant Gaussian background curvature. The Bradlow equation has the peculiarity that on a noncompact manifold, it gives rise to either infinitely many topological vortices or a finite number of nontopological vortices. Finally, I will contemplate possible physical interpretations related to BEC systems with constant magnetic fields.

Riccardo Guida (IPHT Saclay, France)

Title: Theorems from RG flows

Abstract: RG flow equations turn out to be an invaluable tool in proving theorems holding at all loop orders. Mathematically sound results are typically achieved by exploiting the inductive structure of the perturbative flow equations in order to establish bounds on renormalized correlators. I will first overview some remarkable results and then try to convey a few of the main underlying ideas.

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Kenichi Konishi (Universita’ di Pisa)

Title: Strongly-Coupled Infrared Fixed Points, Confinement and Chiral Symmetry Breaking

Abstract: Based on some remarkable developments in understanding N=2 superconformal theories, we review and discuss the concept that confinement may arise as a deformation of a nearby conformally invariant infrared-fixed-point vacuum, described by strongly-coupled nonlocal set of monopoles, dyons and quarks. I point out that there is an intriguing analogy between the most singular N=2 SQCD vacua, perturbed by some mass deformations, and what seems to be happening in the real-world QCD.

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Steffen Krusch (Kent University, UK)

Title: Quantisation of Skyrmions

Abstract: In this talk, I will review the Skyrme model and how a classical scalar field theory can describe atomic nuclei. I also comment on recent developments such as vibrational quantisation.
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Muneto Nitta (Keio University, Japan)

Title: Modulated Vacua

Abstract: Spatial modulation has been studied for a long time in condensed matter, nuclear matter and quark matter, so far in non-relativistic field theories. Here, spatially modulated vacua are studied in relativistic field theories. In our simple model, we find that a Nambu-Goldstone (NG) boson associated with spontaneously broken translational and U(1) symmetries appears without a canonical kinetic (quadratic derivative) term in the modulated direction while a Higgs boson appears as a gapless mode. We then embed our model to a supersymmetric theory and study spontaneous supersymmetry breaking in spatially modulated vacua. We show that there appears a Goldstino associated with the supersymmetry breaking at a meta-stable vacuum, where energy is positive, while it becomes a fermionic ghost in the negative energy vacuum, and zero norm state and disappears from the physical sector in the zero energy vacuum.

Nicodemo Magnoli (Universita' di Genova)

Title: Conformal perturbation of off­critical correlators in the 3D Ising universality class

Abstract: Thanks to the progress of conformal bootstrap methods we have now very precise estimates of both scaling dimensions and OPE coefficients for several 3D universality classes. We show how to use this information to obtain similarly precise estimates for off­critical correlators using conformal perturbation theory. We discuss in particular the < σ(r)σ(0) > two point function in the high and low temperature regimes of the 3D Ising model and evaluate the leading and next to leading terms in the s = tr∆t expansion, where t is the reduced temperature. Our results for < σ(r)σ(0) > agree both with Monte Carlo simulations and with a set of experimental estimates of the critical scattering function.

Title: SYK Model and Schwarzian theory

Abstract: We will present, from a geometrical perspective, some recent results on the Schwarzian theory in connection with the SYK model.

Keisuke Ohashi (Keio University, Japan)

Title: Conformal symmetry of trapped Bose­Einstein condensates and massive Nambu­Goldstone modes

Abstract: The Gross­Pitaevskii (GP) or nonlinear Schrodinger equation relevant to ultracold atomic gaseous Bose­Einstein condensates possess a modified Schrodinger symmetry in two spatial dimensions, in the presence of a harmonic trapping potential, an (artificial) constant magnetic field (or rotation) and an electric field of a quadratic electrostatic potential. We find that a variance and a center of a trapped gas with or without a vorticity can be regarded as massive Nambu­Goldstone (NG) modes associated with spontaneous breaking of the modified Schrodinger symmetry. We show that the Noether theorem for the modified Schrodinger symmetry gives universal equations of motion which describe exact time­evolutions of the trapped gases such as a harmonic oscillation, a cyclotron motion and a breathing oscillation with frequencies determined by the symmetry independently of the details of the system. We further construct an exact eﬀective action for all the NG modes.

Silvia Penati (Universita’ di Milano Bicocca)

Title: Puzzles in 3D Chern-Simons-matter theories

Abstract: I will present a number of solved and unsolved puzzles that arise in N=6 ABJ(M) and N=4 Chern-Simons-matter theories in three dimensions, when evaluating supersymmetric Wilson loops via localization, perturbation theory and holographic methods.

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Eliezer Rabinovici (Hebrew University of Jerusalem, Israel)

Title: On Singularities, Quantum Noise and holographic Complexity ­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­

Norisuke Sakai (Keio University, Japan)

Title: Exact Resurgence Structure to All Orders of Multi­bions in Deformed SUSY Quantum Mechanics

Abstract: Resurgence gives a deep relation between divergent perturbation series to nonperturbative contributions such as bions. Taking quantum mechanical models originating in 2d non­linear sigma models as examples, we investigate the resurgence structure with emphasis on nearly supersymmetric and quasi­exactly solvable parameter regimes. We obtain exact results for the expansion coefficients of the ground state energy in powers of a supersymmetry­breaking deformation parameter. The first and second expansion coefficients of CP1 quantum mechanics are found to be absolutely convergent series of nonperturbative exponentials corresponding to multi­bions with divergent perturbation series on those backgrounds. We obtain all multi­bion exact solutions for finite time interval in the complexified theory. We succeeded to sum the semi­classical multi­bion contributions to find that they reproduce the exact result supporting the resurgence to all orders. We also discuss the similar resurgence structure in the CP(N­1) quantum mechanics (N>2), the squashed CP1 quantum mechanics, and the sine­Gordon quantum mechanics. This is the first result in quantum mechanical models where the resurgent trans­series structure is verified to all orders in nonperturbative multi­bion contributions. The talk will contain results in T.Fujimori, S.Kamata, T.Misumi, M.Nitta and N.Sakai, Phys. Rev. D94, 105002 (2016) [arXiv:1607.04205 [hep­th]]; Phys. Rev. D95, 105001 (2017) [arXiv:1702.00589 [hep­th]]; arXiv:1705.10483.

Domenico Seminara (Universita' di Firenze)

Title: Wilson lines as superconformal defects in ABJM theory: a formula for the emitted radiation

Abstract: We investigate the simplest operator insertions into 1/2 BPS Wilson loops in N = 6 ABJM theory and investigate their two-point correlators. In this framework, the energy emitted by a heavy moving probe can be exactly obtained from some two-point coefficients of bosonic and fermionic insertions. This allows us to confirm a previous proposal for computing the Bremsstrahlung function in terms of certain supersymmetric circular Wilson loops.  In the derivation of this result we also elucidate the structure of protected multiplets in the relevant superconformal defect theory.
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Paul Sutcliffe (Durham University, UK)

Title: Skyrmion knots in frustrated magnets

Abstract: A magnetic Skyrmion is a stable two­dimensional nanoparticle describing a localized winding of the magnetization in certain magnetic materials. Numerical computations of frustrated magnets predict that Skyrmions can be tied into knots to form new stable three­dimensional nanoparticles. These stable equilibria of twisted loops of Skyrmion strings have an integer­valued topological charge, known as the Hopf charge, that counts the number of particles. Rings are formed for low values of this charge, but for higher values it is energetically favourable to form links and then knots.

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Ryosuke Yoshii (Keio University, Japan)

Title: Self-consistent Exact solutions in Gross-Neveu and CP(N-1) models: Inhomogeneous states and Casimir force

Abstract: In this work we consider a fermionic chain of finite length. Fermions are allowed to interact and are forced to obey boundary conditions, thus altering the process of condensation. Our goal is to explore how this affects the quantum vacuum energy for this system. We approach this problem by using a self-consistent method and observe a nontrivial behaviour in the Casimir force, displaying a switch from an attractive to a repulsive regime. This flip stems from the competition between the attractive contribution from the usual fermionic Casimir effect and a repulsive one coming from the condensate. We also find the connection between the solutions in the Gross-Neveu model and those in the CP(N) model.

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