Spectral walls in multifield kink dynamics

Abstract We show that spectral walls are common phenomena in the dynamics of kinks in (1+1) dimensions. They occur in models based on two or more scalar fields with a nonempty Bogomol’nyi-Prasad-Sommerfield (BPS) sector, hosting two zero modes, where they are one of the main factors governing the soliton dynamics. We also show that spectral walls appear as singularities of the dynamical vibrational moduli space.

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A consistent two-skyrmion configuration space from instantons

Journal of High Energy Physics ◽

10.1007/jhep12(2021)039 ◽

2021 ◽

Vol 2021 (12) ◽

Author(s):

Chris Halcrow ◽

Thomas Winyard

Keyword(s):

Configuration Space ◽

Moduli Space ◽

General Framework ◽

Degrees Of Freedom ◽

Skyrme Model ◽

Low Energy ◽

Nuclear System ◽

Fundamental Properties ◽

Zero Modes ◽

Definition Of

Abstract To study a nuclear system in the Skyrme model one must first construct a space of low energy Skyrme configurations. However, there is no mathematical definition of this configuration space and there is not even consensus on its fundamental properties, such as its dimension. Here, we propose that the full instanton moduli space can be used to construct a consistent skyrmion configuration space, provided that the Skyrme model is coupled to a vector meson which we identify with the ρ-meson. Each instanton generates a unique skyrmion and we reinterpret the 8N instanton moduli as physical degrees of freedom in the Skyrme model. In this picture a single skyrmion has six zero modes and two non-zero modes: one controls the overall scale of the solution and one the energy of the ρ-meson field. We study the N = 1 and N = 2 systems in detail. Two interacting skyrmions can excite the ρ through scattering, suggesting that the ρ and Skyrme fields are intrinsically linked. Our proposal is the first consistent manifold description of the two-skyrmion configuration space. The method can also be generalised to higher N and thus provides a general framework to study any skyrmion configuration space.

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Precise calculation of the decay rate of false vacuum with multi-field bounce

Journal of High Energy Physics ◽

10.1007/jhep11(2020)006 ◽

2020 ◽

Vol 2020 (11) ◽

Cited By ~ 1

Author(s):

So Chigusa ◽

Takeo Moroi ◽

Yutaro Shoji

Keyword(s):

Decay Rate ◽

Scalar Fields ◽

Gauge Fields ◽

Gauge Parameter ◽

False Vacuum ◽

Vacuum Decay ◽

Loop Contribution ◽

Zero Modes ◽

Precise Calculation ◽

The One

Abstract We study the decay rate of a false vacuum in gauge theory at the one-loop level. We pay particular attention to the case where the bounce consists of an arbitrary number of scalar fields. With a multi-field bounce, which has a curved trajectory in the field space, the mixing among the gauge fields and the scalar fields evolves along the path of the bounce in the field space and the one-loop calculation of the vacuum decay rate becomes complicated. We consider the one-loop contribution to the decay rate with an arbitrary choice of the gauge parameter, and obtain a gauge invariant expression of the vacuum decay rate. We also give proper treatments of gauge zero modes and renormalization.

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D-instanton perturbation theory

Journal of High Energy Physics ◽

10.1007/jhep08(2020)075 ◽

2020 ◽

Vol 2020 (8) ◽

Cited By ~ 1

Author(s):

Ashoke Sen

Keyword(s):

Perturbation Theory ◽

Moduli Space ◽

Riemann Surfaces ◽

Open String ◽

Collective Coordinates ◽

Zero Modes ◽

World Volume ◽

Infra Red ◽

Gauge Fixing ◽

Zero Momentum

Abstract D-instanton world-volume theory has open string zero modes describing collective coordinates of the instanton. The usual perturbative amplitudes in the D-instanton background suffer from infra-red divergences due to the presence of these zero modes, and the usual approach of analytic continuation in momenta does not work since all open string states on a D-instanton carry strictly zero momentum. String field theory is well-suited for tackling these issues. However we find a new subtlety due to the existence of additional zero modes in the ghost sector. This causes a breakdown of the Siegel gauge, but a different gauge fixing consistent with the BV formalism renders the perturbation theory finite and unambiguous. At each order, this produces extra contribution to the amplitude besides what is obtained from integration over the moduli space of Riemann surfaces.

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Normal ordering normal modes

The European Physical Journal C ◽

10.1140/epjc/s10052-021-08890-7 ◽

2021 ◽

Vol 81 (1) ◽

Cited By ~ 1

Author(s):

Jarah Evslin

Keyword(s):

Plane Waves ◽

Recursion Formula ◽

Normal Modes ◽

Scalar Fields ◽

Quantum Field ◽

Expectation Values ◽

Normal Ordering ◽

Zero Modes ◽

The One ◽

Schrödinger Picture

AbstractIn a soliton sector of a quantum field theory, it is often convenient to expand the quantum fields in terms of normal modes. Normal mode creation and annihilation operators can be normal ordered, and their normal ordered products have vanishing expectation values in the one-loop soliton ground state. The Hamiltonian of the theory, however, is usually normal ordered in the basis of operators which create plane waves. In this paper we find the Wick map between the two normal orderings. For concreteness, we restrict our attention to Schrodinger picture scalar fields in 1+1 dimensions, although we expect that our results readily generalize beyond this case. We find that plane wave ordered n-point functions of fields are sums of terms which factorize into j-point functions of zero modes, breather and continuum normal modes. We find a recursion formula in j and, for products of fields at the same point, we solve the recursion formula at all j.

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ON REAL INTRINSIC WALL CROSSINGS

International Journal of Modern Physics A ◽

10.1142/s0217751x11054917 ◽

2011 ◽

Vol 26 (30n31) ◽

pp. 5171-5209 ◽

Cited By ~ 1

Author(s):

STEFANO BELLUCCI ◽

BHUPENDRA NATH TIWARI

Keyword(s):

Phase Transition ◽

Scalar Curvature ◽

Moduli Space ◽

Riemannian Geometry ◽

Scalar Fields ◽

Leading Order ◽

Geometric Methods ◽

Phase Structures ◽

Global Nature ◽

The Stability

We study moduli space stabilization of a class of BPS configurations from the perspective of the real intrinsic Riemannian geometry. Our analysis exhibits a set of implications towards the stability of the D-term potentials, defined for a set of Abelian scalar fields. In particular, we show that the nature of marginal and threshold walls of stabilities may be investigated by real geometric methods. Interestingly, we find that the leading order contributions may easily be accomplished by translations of the Fayet parameter. Specifically, we notice that the various possible linear, planar, hyperplanar and the entire moduli space stability may easily be reduced to certain polynomials in the Fayet parameter. For a set of finitely many real scalar fields, it may be further inferred that the intrinsic scalar curvature defines the global nature and range of vacuum correlations. Whereas, the underlying moduli space configuration corresponds to a noninteracting basis at the zeros of the scalar curvature, where the scalar fields become uncorrelated. The divergences of the scalar curvature provide possible phase structures, viz., wall of stability, phase transition, if any, in the chosen moduli configuration. The present analysis opens up a new avenue towards the stabilization of gauge and string moduli.

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DOMAIN WALLS WITH NON-ABELIAN FLAVOR SYMMETRY

International Journal of Modern Physics A ◽

10.1142/s0217751x08040895 ◽

2008 ◽

Vol 23 (14n15) ◽

pp. 2234-2236

Author(s):

TOSHIAKI FUJIMORI

Keyword(s):

Field Theory ◽

Effective Field Theory ◽

Moduli Space ◽

Domain Walls ◽

Bound State ◽

Effective Field ◽

Repulsive Force ◽

Flavor Symmetry ◽

Zero Modes ◽

Goldstone Modes

Domain walls in gauge theory with non-Abelian flavor symmetry possess normalizable Nambu-Goldstone zero modes associated with spontaneously broken non-Abelian flavor symmetry. We construct the moduli space metric as the effective field theory of walls. The Nambu-Goldstone modes spread between two domain walls and their rotation induces long-range repulsive force. We also construct a bound state of domain walls. This article is based on the work with M. Eto, M. Nitta, K. Ohashi and N. Sakai1.

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SCALAR AND FERMION ZERO MODES ON THE THICK BRANE ARISING FROM TWO SCALAR FIELDS

Modern Physics Letters A ◽

10.1142/s0217732308026492 ◽

2008 ◽

Vol 23 (37) ◽

pp. 3179-3186

Author(s):

MUYUN DU ◽

XIYUN DU ◽

YUEYING XIE

Keyword(s):

Yukawa Coupling ◽

Scalar Fields ◽

Zero Modes ◽

Fermionic Fields

In this note we study scalar and fermion zero modes on the brane arising from two scalar fields. The result is that there exist normalizable massless modes of scalar fields which can be localized on the brane. While, for spin 1/2 and spin 3/2 fermions, the corresponding zero modes are non-normalizable. Thus, some mechanism such as Yukawa coupling should be introduced for the localization of these fermionic fields on the thick brane.

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Dynamical Cobordism and Swampland Distance Conjectures

Journal of High Energy Physics ◽

10.1007/jhep10(2021)037 ◽

2021 ◽

Vol 2021 (10) ◽

Author(s):

Ginevra Buratti ◽

José Calderón-Infante ◽

Matilda Delgado ◽

Angel M. Uranga

Keyword(s):

Moduli Space ◽

Domain Walls ◽

Scalar Fields ◽

Recent Proposal ◽

Run Off ◽

Finite Distance ◽

Scalar Potentials ◽

M Theory ◽

Space Distance ◽

Finite Extent

Abstract We consider spacetime-dependent solutions to string theory models with tadpoles for dynamical fields, arising from non-trivial scalar potentials. The solutions have necessarily finite extent in spacetime, and are capped off by boundaries at a finite distance, in a dynamical realization of the Cobordism Conjecture. We show that as the configuration approaches these cobordism walls of nothing, the scalar fields run off to infinite distance in moduli space, allowing to explore the implications of the Swampland Distance Conjecture. We uncover new interesting scaling relations linking the moduli space distance and the SDC tower scale to spacetime geometric quantities, such as the distance to the wall and the scalar curvature. We show that walls at which scalars remain at finite distance in moduli space correspond to domain walls separating different (but cobordant) theories/vacua; this still applies even if the scalars reach finite distance singularities in moduli space, such as conifold points.We illustrate our ideas with explicit examples in massive IIA theory, M-theory on CY threefolds, and 10d non-supersymmetric strings. In 4d $$ \mathcal{N} $$ N = 1 theories, our framework reproduces a recent proposal to explore the SDC using 4d string-like solutions.

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