arXiv subjects

Stefano Bolognesi

Publications and source records attributed to Stefano Bolognesi.

At least 55 records · Page 3Linked to original sources

arXiv2018

Patterns of Symmetry Breaking in Chiral "QCD"

We consider $SU(N)$ Yang-Mills theory with massless chiral fermions in a complex representation of the gauge group. The main emphasis is on the so-called hybrid psi-chi-eta model. The possible patterns of realization of the continuous chiral flavor symmetry are discussed. We argue that the chiral symmetry is broken in conjunction with a dynamical Higgsing of the gauge group (complete or partial) by bi-fermion condensates. As a result a color-flavor locked symmetry is preserved. The 't Hooft anomaly matching proceeds via saturation of triangles by massless composite fermions or, in a mixed mode, i.e., also by the "weakly" coupled fermions associated with dynamical Abelianization, supplemented by a number of Nambu-Goldstone mesons. Gauge-singlet condensates are of the multifermion type and, though it cannot be excluded, the chiral symmetry realization via such gauge invariant condensates is more contrived (requires a number of four-fermion condensates simultaneously and, even so, problems remain), and less plausible. We conclude that in the model at hand, chiral flavor symmetry implies dynamical Higgsing by bifermion condensates.

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arXiv2018

Large-$N$ $\mathbb{CP}^{N-1}$ sigma model on a finite interval: general Dirichlet boundary conditions

This is the third of the series of articles on the large-$N$ two-dimensional $\mathbb{CP}^{N-1}$ sigma model, defined on a finite space interval $L$ with Dirichlet boundary conditions. Here the cases of the general Dirichlet boundary conditions are studied, where the relative $\mathbb{CP}^{N-1}$ orientations at the two boundaries are generic, and numerical solutions are presented. Distinctive features of the $\mathbb{CP}^{N-1}$ sigma model, as compared e.g., to an $O(N)$ model, which were not entirely evident in the basic properties studied in the first two articles in the large $N$ limit, manifest themselves here. It is found that the total energy is minimized when the fields are aligned in the same direction at the two boundaries.

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arXiv2018

Large-N CP(N-1) sigma model on a finite interval and the renormalized string energy

We continue the analysis started in a recent paper of the large-N two-dimensional CP(N-1) sigma model, defined on a finite space interval L with Dirichlet (or Neumann) boundary conditions. Here we focus our attention on the problem of the renormalized energy density $\mathcal{E}(x,Λ,L)$ which is found to be a sum of two terms, a constant term coming from the sum over modes, and a term proportional to the mass gap. The approach to $\mathcal{E}(x,Λ,L)\to\tfrac{N}{4π}Λ^2$ at large $LΛ$ is shown, both analytically and numerically, to be exponential: no power corrections are present and in particular no Lüscher term appears. This is consistent with the earlier result which states that the system has a unique massive phase, which interpolates smoothly between the classical weakly-coupled limit for $LΛ\to 0$ and the "confined" phase of the standard CP(N-1) model in two dimensions for $LΛ\to\infty$.

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arXiv2017

From the Sakai-Sugimoto Model to the Generalized Skyrme Model

We derive the generalized Skyrme model as a low-energy effective model of the Sakai-Sugimoto model. The novelty with the past is the presence of the sextic term equal to the topological charge squared. This term appears when the $ω$ meson, and the tower of states on top of it, are integrated out. We claim that, in the small 't Hooft coupling limit, the instanton is well described by a Skyrmion arising from the low energy effective Lagrangian of the Sakai-Sugimoto model. The sextic term plays a dominant role in this limit. Moreover, when a pion mass term is added we recover the BPS Skyrme model in the small 't Hooft coupling limit.

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arXiv2017

A Solitonic Approach to Holographic Nuclear Physics

We discuss nuclear physics in the Sakai-Sugimoto model in the limit of large number $N_c$ of colors and large 't Hooft coupling $λ$. In this limit the individual baryons are described by classical solitons whose size is much smaller than the typical distance at which they settle in a nuclear bound state. We can thus use the linear approximation outside the instanton cores to compute the interaction potential. We find the classical geometry of nuclear bound states for baryon number up to eight. One of the interesting features that we find is that holographic nuclear physics provides a natural description for lightly bound states when $λ$ is large. For the case of two nuclei, we also find the topology and metric of the manifold of zero modes and, quantizing it, we find that the ground state can be identified with the deuteron state. We discuss the relations with other methods in the literature used to study Skyrmions and holographic nuclear physics. We discuss $1/{N_c}$ and $1/λ$ corrections and the challenges to overcome to reach the phenomenological values to fit with real QCD.

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arXiv2016

Theta dependence in Holographic QCD

We study the effects of the CP-breaking topological $θ$-term in the large $N_c$ QCD model by Witten, Sakai and Sugimoto with $N_f$ degenerate light flavors. We first compute the ground state energy density, the topological susceptibility and the masses of the lowest lying mesons, finding agreement with expectations from the QCD chiral effective action. Then, focusing on the $N_f=2$ case, we consider the baryonic sector and determine, to leading order in the small $θ$ regime, the related holographic instantonic soliton solutions. We find that while the baryon spectrum does not receive ${\cal O}(θ)$ corrections, 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. Finally, we compute the CP-violating pion-nucleon coupling constant ${\bar g}_{πN N}$, finding that it is zero to leading order in the large $N_c$ limit.

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arXiv2016

Neutron electric dipole moment from gauge/string duality

We compute the electric dipole moment of nucleons in the large $N_c$ QCD model by Witten, Sakai and Sugimoto with $N_f=2$ degenerate massive flavors. Baryons in the model are instantonic solitons of an effective five-dimensional action describing the whole tower of mesonic fields. We find that the dipole electromagnetic form factor of the nucleons, induced by a finite topological $θ$ angle, exhibits complete vector meson dominance. We are able to evaluate the contribution of each vector meson to the final result - a small number of modes are relevant to obtain an accurate estimate. Extrapolating the model parameters to real QCD data, the neutron electric dipole moment is evaluated to be $d_n = 1.8 \cdot 10^{-16}\, θ\;e\cdot \mathrm{cm}$. The electric dipole moment of the proton is exactly the opposite.

hep-ph↗

arXiv2016

Large-N CP(N-1) sigma model on a finite interval: physical boundary effects

We analyze the two-dimensional CP(N-1) sigma model defined on a finite space interval L, with various boundary conditions, in the large N limit. With the Dirichlet boundary condition at the both ends, we show that the system has a unique phase, which smoothly approaches in the large L limit the standard 2D CP(N-1) sigma model in confinement phase, with a constant mass generated for the n(i) fields. We study the full functional saddle-point equations for finite L, and solve them numerically. The latter reduces to the well-known gap equation in the large L limit. It is found that the solution satisfies actually both the Dirichlet and Neumann conditions.

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arXiv2016

A Cosmology of a Trans-Planckian Theory and Dark Energy

We investigate a model based on a generalised version of the Fourier transform for curved space-time manifolds. This model is possible if the metric has an asymptotic flat region which allows a duality to be implement between coordinates and momenta, hence, the models's name, trans-Planckian. The theory and the action are based on the postulate of the absolute egalitarian relation between coordinates $x$ and momenta $p$. We show how to implement this construction in a cosmological setting, on a Friedman-Robertson-Walker metric background, where the asymptotic time infinity plays the role of the required asymptotic flat region. We discuss the effect of gravity, and, in particular, of the Hubble expansion of the universe scale factor on the Fourier map. The dual inflationary stage is responsible for making the dual sector of the action inaccessible at ordinary low energies. We propose a scenario in which an effective positive cosmological constant is caused by how the dual sector of the theory affects the equation of state for matter particles.

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arXiv2016

String pair production in non homogeneous backgrounds

We consider string pair production in non homogeneous electric backgrounds. We study several particular configurations which can be addressed with the Euclidean world-sheet instanton technique, the analogue of the world-line instanton for particles. In the first case the string is suspended between two D-branes in flat space-time, in the second case the string lives in AdS and terminates on one D-brane (this realizes the holographic Schwinger effect). In some regions of parameter space the result is well approximated by the known analytical formulas, either the particle pair production in non-homogeneous background or the string pair production in homogeneous background. In other cases we see effects which are intrinsically stringy and related to the non-homogeneity of the background. The pair production is enhanced already for particles in time dependent electric field backgrounds. The string nature enhances this even further. For spacial varying electrical background fields the string pair production is less suppressed than the rate of particle pair production. We discuss in some detail how the critical field is affected by the non-homogeneity, for both time and space dependent electric field backgrouds. We also comment on what could be an interesting new prediction for the small field limit. The third case we consider is pair production in holographic confining backgrounds with homogeneous and non-homogeneous fields.

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arXiv2015

$\mathcal{N}=2$ Argyres-Douglas theories, $\mathcal{N}=1$ SQCD and Seiberg duality

We revisit the study of singular points in the Coulomb branch of $\mathcal{N}=2$ SQCD in four dimensions with gauge group $SU(N)$ and odd number of flavors. For certain choices of the mass parameters these vacua are not lifted by a mass term for the chiral multiplet in the adjoint representation. By using recent results about the M5 brane description of $\mathcal{N}=1$ theories we study the resulting vacua and argue that the low-energy effective theory has a simple Lagrangian description involving a free chiral multiplet in the adjoint representation of the flavor symmetry group, a system somewhat reminiscent of the standard low-energy pion description of the real-world QCD. This fact is quite remarkable in view of the fact that the underlying $\mathcal{N}=2$ SCFT (the Argyres-Douglas systems) are strongly-coupled non-local theories of quarks and monopoles.

hep-th↗

arXiv2015

Geometry and Dynamics of a Coupled 4D-2D Quantum Field Theory

Geometric and dynamical aspects of a coupled 4D-2D interacting quantum field theory - the gauged nonAbelian vortex - are investigated. The fluctuations of the internal 2D nonAbelian vortex zeromodes excite the massless 4D Yang-Mills modes and in general give rise to divergent energies. This means that the well-known 2D CP(N-1) zeromodes associated with a nonAbelian vortex become nonnormalizable. Moreover, all sorts of global, topological 4D effects such as the nonAbelian Aharonov-Bohm effect come into play. These topological global features and the dynamical properties associated with the fluctuation of the 2D vortex moduli modes are intimately correlated, as shown concretely here in a U(1) x SU(N) x SU(N) model with scalar fields in a bifundamental representation of the two SU(N) factor gauge groups.

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arXiv2015

Magnetic bags in hyperbolic space

A magnetic bag is an abelian approximation to a large number of coincident SU(2) BPS monopoles. In this paper we consider magnetic bags in hyperbolic space and derive their Nahm transform from the large charge limit of the discrete Nahm equation for hyperbolic monopoles. An advantage of studying magnetic bags in hyperbolic space, rather than Euclidean space, is that a range of exact charge N hyperbolic monopoles can be constructed, for arbitrarily large values of N, and compared with the magnetic bag approximation. We show that a particular magnetic bag (the magnetic disc) provides a good description of the axially symmetric N-monopole. However, an abelian magnetic bag is not a good approximation to a roughly spherical N-monopole that has more than N zeros of the Higgs field. We introduce an extension of the magnetic bag that does provide a good approximation to such monopoles and involves a spherical non-abelian interior for the bag, in addition to the conventional abelian exterior.

hep-th↗

arXiv2015

NonAbelian Vortices, Large Winding Limits and Aharonov-Bohm Effects

Remarkable simplification arises from considering vortex equations in the large winding limit. This was recently used in [1] to display all sorts of vortex zeromodes, the orientational, translational, fermionic as well as semi-local, and to relate them to the apparently distinct phenomena of the Nielsen-Olesen-Ambjorn magnetic instabilities. Here we extend these analyses to more general types of BPS nonAbelian vortices, taking as a prototype a system with gauged U(1) x SU(N) x SU(N) symmetry where the VEV of charged scalar fields in the bifundamental representation breaks the symmetry to SU(N)_{l+r} . The presence of the massless SU(N)_{l+r} gauge fields in 4D bulk introduces all sorts of non-local, topological phenomena such as the nonAbelian Aharonov-Bohm effects, which in the theory with global SU(N)_r group (g_r=0) are washed away by the strongly fluctuating orientational zeromodes in the worldsheet. Physics changes qualitatively at the moment the right gauge coupling constant g_r is turned on.

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arXiv2014

Vortex Zero Modes, Large Flux Limit and Ambjørn-Nielsen-Olesen Magnetic Instabilities

In the large flux limit vortices become flux tubes with almost constant magnetic field in the interior region. This occurs in the case of non-Abelian vortices as well, and the study of such configurations allows us to reveal a close relationship between vortex zero modes and the gyromagnetic instabilities of vector bosons in a strong background magnetic field discovered by Nielsen, Olesen and Ambjørn. The BPS vortices are exactly at the onset of this instability, and the dimension of their moduli space is precisely reproduced in this way. We present a unifying picture in which, through the study of the linear spectrum of scalars, fermions and W bosons in the magnetic field background, the expected number of translational, orientational, fermionic as well as semilocal zero modes is correctly reproduced in all cases.

hep-th↗

arXiv2014

Hyperbolic monopoles, JNR data and spectral curves

A large class of explicit hyperbolic monopole solutions can be obtained from JNR instanton data, if the curvature of hyperbolic space is suitably tuned. Here we provide explicit formulae for both the monopole spectral curve and its rational map in terms of JNR data. Examples with platonic symmetry are presented, together with some one-parameter families with cyclic and dihedral symmetries. These families include hyperbolic analogues of geodesics that describe symmetric monopole scatterings in Euclidean space and we illustrate the results with energy density isosurfaces. There is a metric on the moduli space of hyperbolic monopoles, defined using the abelian connection on the boundary of hyperbolic space, and we provide a simple integral formula for this metric on the space of JNR data.

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arXiv2013

A low-dimensional analogue of holographic baryons

Baryons in holographic QCD correspond to topological solitons in the bulk. The most prominent example is the Sakai-Sugimoto model, where the bulk soliton in the five-dimensional spacetime of AdS-type can be approximated by the flat space self-dual Yang-Mills instanton with a small size. Recently, the validity of this approximation has been verified by comparison with the numerical field theory solution. However, multi-solitons and solitons with finite density are currently beyond numerical field theory computations. Various approximations have been applied to investigate these important issues and have led to proposals for finite density configurations that include dyonic salt and baryonic popcorn. Here we introduce and investigate a low-dimensional analogue of the Sakai-Sugimoto model, in which the bulk soliton can be approximated by a flat space sigma model instanton. The bulk theory is a baby Skyrme model in a three-dimensional spacetime with negative curvature. The advantage of the lower-dimensional theory is that numerical simulations of multi-solitons and finite density solutions can be performed and compared with flat space instanton approximations. In particular, analogues of dyonic salt and baryonic popcorn configurations are found and analysed.

hep-th↗

arXiv2013

The Sakai-Sugimoto soliton

The Sakai-Sugimoto model is the preeminent example of a string theory description of holographic QCD, in which baryons correspond to topological solitons in the bulk. Here we investigate the validity of various approximations of the Sakai-Sugimoto soliton that are used widely to study the properties of holographic baryons. These approximations include the flat space self-dual instanton, a linear expansion in terms of eigenfunctions in the holographic direction and an asymptotic power series at large radius. These different approaches have produced contradictory results in the literature regarding properties of the baryon, such as relations for the electromagnetic form factors. Here we determine the regions of validity of these various approximations and show how to relate different approximations in contiguous regions of applicability. This analysis clarifies the source of the contradictory results in the literature and resolves some outstanding issues, including the use of the flat space self-dual instanton, the detailed properties of the asymptotic soliton tail, and the role of the UV cutoff introduced in previous investigations. A consequence of our analysis is the discovery of a new large scale, that grows logarithmically with the 't Hooft coupling, at which the soliton fields enter a nonlinear regime. Finally, we provide the first numerical computation of the Sakai-Sugimoto soliton and demonstrate that the numerical results support our analysis.

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