Wess-Zumino Term Research Articles

Skyrmions, half-skyrmions and nucleon mass in dense baryonic matter

We explore the hadron properties in dense baryonic matter in a unified way by using a Skyrme model constructed with an effective Lagrangian which includes the ρ and ω vector mesons as hidden gauge bosons and is valid up to O(p4) in chiral expansion including the homogeneous Wess-Zumino terms. With the two input values of pion decay constant and the lowest lying vector meson mass which can be fixed in free space, all the other low energy constants in the effective Lagrangian are determined by their master formulas derived from holographic QCD models, which allows us to study the baryonic matter properties with no additional free parameters and thus without ambiguities. We find that the ω field that figures in the homogeneous Wess-Zumino term plays a crucial role in the skyrmion structure and its matter properties. The most striking and intriguing observation is that the pion decay constant that smoothly drops with increasing density in the Skyrmion phase stops decreasing at n1/2 at which the skyrmions in medium fractionize into half-skyrmions and remains nearly constant in the half-skyrmion phase. In accordance with the large Nc consideration, the baryon mass also stays non-scaling in the half-skyrmion phase. This feature is supported by the nuclear effective field theory with the parameters of the Lagrangian scaling modified at the skyrmion–half-skyrmion phase transition. Our exploration also uncovers the crucial role of the ω meson in multi-baryon systems as well as in the structure of a single skyrmion.

Holography and conformal anomaly matching

We discuss various issues related to the understanding of the conformal anomaly matching in CFT from the dual holographic viewpoint. First, we act with a PBH diffeomorphism on a generic 5D RG flow geometry and show that the corresponding on-shell bulk action reproduces the Wess-Zumino term for the dilaton of broken conformal symmetry, with the expected coefficient aUV-aIR. Then we consider a specific 3D example of RG flow whose UV asymptotics is normalizable and admits a 6D lifting. We promote a modulus \rho appearing in the geometry to a function of boundary coordinates. In a 6D description {\rho} is the scale of an SU(2) instanton. We determine the smooth deformed background up to second order in the space-time derivatives of \rho and find that the 3D on-shell action reproduces a boundary kinetic term for the massless field \tau= log(\rho) with the correct coefficient \delta c=cUV-cIR. We further analyze the linearized fluctuations around the deformed background geometry and compute the one-point functions <T\mu\nu> and show that they are reproduced by a Liouville-type action for the massless scalar \tau, with background charge due to the coupling to the 2D curvature R. The resulting central charge matches \delta c. We give an interpretation of this action in terms of the (4,0) SCFT of the D1-D5 system in type I theory.

Dense baryonic matter in the hidden local symmetry approach: Half-skyrmions and nucleon mass

Hadron properties in dense medium are treated in a unified way in a skyrmion model constructed with an effective Lagrangian, in which the $\ensuremath{\rho}$ and $\ensuremath{\omega}$ vector mesons are introduced as hidden gauge bosons, valid up to $O({p}^{4})$ terms in chiral expansion including the homogeneous Wess-Zumino terms. All the low energy constants of the Lagrangian---apart from the pion decay constant and the vector meson mass---are fixed by the master formula derived from the relation between the five-dimensional holographic QCD and the four-dimensional hidden local symmetry Lagrangian. This Lagrangian allows one to pin down the density ${n}_{1/2}$ at which the skyrmions in medium fractionize into half-skyrmions, bringing in a drastic change in the equation of state of dense baryonic matter. We find that the $U(1)$ field that figures in the Chern-Simons term in the five-dimensional holographic QCD action or equivalently the $\ensuremath{\omega}$ field in the homogeneous Wess-Zumino term in the dimensionally reduced hidden local symmetry action plays a crucial role in the half-skyrmion phase. The importance of the $\ensuremath{\omega}$ degree of freedom may be connected to what happens in the instanton structure of elementary baryon noticed in holographic QCD. The most striking and intriguing in what is found in the model is that the pion decay constant that smoothly drops with increasing density in the skyrmion phase stops decreasing at ${n}_{1/2}$ and remains nearly constant in the half-skyrmion phase. In accordance with the large ${N}_{c}$ consideration, the baryon mass also stays nonscaling in the half-skyrmion phase. This feature which is reminiscent of the parity-doublet baryon model with a chirally invariant mass ${m}_{0}$ is supported by the nuclear effective field theory with the parameters of the Lagrangian scaling modified at the skyrmion--half-skyrmion phase transition. It also matches with one-loop renormalization group analysis based on hidden local symmetry. A link between a nonvanishing ${m}_{0}$ and the origin of nucleon mass distinctive from dynamically generated mass is suggested. We briefly discuss the possible consequences of the topology change found in this paper on the forthcoming experiments at the rare isotope beam machines under construction.

THE GAUGING OF TWO-DIMENSIONAL BOSONIC SIGMA MODELS ON WORLD-SHEETS WITH DEFECTS

We extend our analysis of the gauging of rigid symmetries in bosonic two-dimensional sigma models with Wess–Zumino terms in the action to the case of world-sheets with defects. A structure that permits a non-anomalous coupling of such sigma models to world-sheet gauge fields of arbitrary topology is analyzed, together with obstructions to its existence, and the classification of its inequivalent choices.

Contractions of AdS brane algebra and superGalileon Lagrangians

We examine AdS Galileon Lagrangians using the method of nonlinear realization. By contractions (1) flat curvature limit, (2) non-relativistic brane algebra limit, and (3) (1) + (2) limits we obtain DBI, Newton-Hoock, and Galilean Galileons, respectively. We make clear how these Lagrangians appear as invariant 4-forms and/or pseudo-invariant Wess-Zumino (WZ) terms using Maurer-Cartan (MC) equations on the coset G/SO(3, 1). We show the equations of motion are written in terms of the MC forms only and explain why the inverse Higgs condition is obtained as the equation of motion for all cases. The supersymmetric extension is also examined using a supercoset SU(2, 2|1)/(SO(3, 1) × U(1)) and five WZ forms are constructed. They are reduced to the corresponding five Galileon WZ forms in the bosonic limit and are candidates for supersymmetric Galileon action.

Non-Abelian tensor towers and (2,0) superconformal theories

With the aim to study six-dimensional (2, 0) superconformal theories with non-Abelian tensor multiplets we propose a five-dimensional superconformal action with eight supersymmetries for an infinite tower of non-Abelian vector, tensor and hypermultiplets. It describes the dynamics of the complete spectrum of the (2, 0) theories compactified on a circle coupled to an additional vector multiplet containing the circle radius and the Kaluza-Klein vector arising from the six-dimensional metric. All couplings are only given in terms of group theoretical constants and the Kaluza-Klein levels. After superconformal symmetry is reduced to Poincaré supersymmetry we find a Kaluza-Klein inspired action coupling super-Yang-Mills theory to an infinite tower of massive non-Abelian tensors. We explore the possibility to restore sixteen supersymmetries by using techniques known from harmonic superspace. Namely, additional bosonic coordinates on a four-sphere are introduced to enhance the R-symmetry group. Maximally supersymmetric Yang-Mills theories and the Abelian (2, 0) tensor theories are recovered as special cases of our construction. Finally, we comment on the generation of an anomaly balancing Wess-Zumino term for the R-symmetry vector at one loop.

RG flows in d dimensions, the dilaton effective action, and the a-theorem

Motivated by the recent dilaton-based proof of the 4d a-theorem, we study the dilaton effective action for RG flows in d dimensions. When d is even, the action consists of a Wess-Zumino (WZ) term, whose Weyl-variation encodes the trace-anomaly, plus all Weyl-invariants. For d odd, the action consists of Weyl-invariants only. We present explicit results for the flat-space limit of the dilaton effective action in d-dimensions up to and including 8-derivative terms. GJMS-operators from conformal geometry motivate a form of the action that unifies the Weyl-invariants and anomaly-terms into a compact general-d structure. A new feature in 8d is the presence of an 8-derivative Weyl-invariant that pollutes the O(p^8)-contribution from the WZ action to the dilaton scattering amplitudes; this may challenge a dilaton-based proof of an a-theorem in 8d. We use the example of a free massive scalar for two purposes: 1) it allows us to confirm the structure of the d-dimensional dilaton effective action explicitly; we carry out this check for d=3,4,5,...,10; and 2) in 8d we demonstrate how the flow (a_UV - a_IR) can be extracted systematically from the O(p^8)-amplitudes despite the contamination from the 8-derivative Weyl-invariant. This computation gives a value for the a-anomaly of the 8d free conformal scalar that is shown to match the value obtained from zeta-function regularization of the log-term in the free energy.

Skyrmions with vector mesons in the hidden local symmetry approach

The roles of light $\rho$ and $\omega$ vector mesons in the Skyrmion are investigated in a chiral Lagrangian derived from the hidden local symmetry (HLS) up to $O(p^4)$ including the homogeneous Wess-Zumino (hWZ) terms. We write a general "master formula" that allows us to determine the parameters of the HLS Lagrangian from a class of holographic QCD models valid at large $N_c$ and $\lambda$ ('t Hooft constant) limit by integrating out the infinite towers of vector and axial-vector mesons other than the lowest $\rho$ and $\omega$ mesons. Within this approach we find that the physical properties of the Skyrmion as the solitonic description of baryons are \textit{independent} of the HLS parameter $a$. Therefore the only parameters of the model are the pion decay constant and the vector meson mass. Once determined in the meson sector, we have a totally parameter-free theory that allows us to study unequivocally the role of light vector mesons in the Skyrmion structure. We find, as suggested by Sutcliffe, that inclusion of the $\rho$ meson reduces the soliton mass, which makes the Skyrmion come closer to the Bogomol'nyi-Prasad-Sommerfield (BPS) soliton, but the role of the $\omega$ meson is found to increase the soliton mass. In a stark contrast, the $\Delta$-$N$ mass difference, which is determined by the moment of inertia in adiabatic collective quantization of the Skyrmion, is increased by the $\rho$ vector meson, while it is reduced by the inclusion of the $\omega$ meson. All these observations show the importance of the $\omega$ meson in the properties of the nucleon and nuclear matter in the Skyrme model.

Can the nucleon axial charge be ?

The nucleon self-energy and its relation to the nucleon axial charge gA are discussed at large Nc. The energy is compared for the hedgehog, conventional, and recently proposed dichotomous nucleon wavefunctions which give different values for gA. We consider their energies at both perturbative and non-perturbative levels. In perturbative estimates, we take into account the pion exchanges among quarks up to the third orders of axial charge vertices, including the many-body forces such as the Wess-Zumino terms. It turns out that the perturbative pion exchanges among valence quarks give the same leading Nc contributions for three wavefunctions, while their mass differences are O(Lamba_qcd). The signs of splittings flip for different orders of the axial charge vertices, so it is hard to conclude which one is the most energetically favored. For non-perturbative estimates involving the modification of quark bases, we use the chiral quark soliton model as an illustration. With the hedgehog quark wavefunctions with gA of O(Nc), we investigate whether solutions with coherent pions are energetically favored. Again it is hard to give decisive conclusions, but it is likely that adding the confining effects disfavors the solution with the coherent pions, making a pion cloud around a nucleon quantum rather than coherent. The nuclear matter at large Nc is also discussed in light of the value of gA.

Path Integral Quantization of Superparticle with 1/4 Supersymmetry Breaking

We present path integral quantization of a massive superparticle in d =4 which preserves 1/4 of the target space supersymmetry with eight supercharges, and so corresponds to the partial breaking N = 8 to N = 2. Its worldline action contains a Wess-Zumino term, explicitly breaks d =4 Lorentz symmetry and exhibits one complex fermionic k-symmetry. We perform the Hamilton-Jacobi formalism of constrained systems, to obtain the equations of motion of the model as total differential equations in many variables. These equations of motion are in exact agreement with those obtained by Dirac’s method.

SO(9) supergravity in two dimensions

Abstract We present maximal supergravity in two dimensions with gauge group SO(9). The construction is based on selecting the proper embedding of the gauge group into the infinite-dimensional symmetry group of the ungauged theory. The bosonic part of the Lagrangian is given by a (dilaton-)gravity coupled non-linear gauged σ-model with Wess-Zumino term. We give explicit expressions for the fermionic sector, the Yukawa couplings and the scalar potential which supports a half-supersymmetric domain wall solution. The theory is expected to describe the low-energy effective action upon reduction on the D0-brane near-horizon warped AdS 2 ×S 8 geometry, dual to the supersymmetric (BFSS) matrix quantum mechanics.

Instant-Form and Light-Front Hamiltonian and Path Integral Formulations of the Conformally Gauge-Fixed Polyakov D1-Brane Action in the Presence of a Scalar Axion Field and an &amp;lt;i&amp;gt;U&amp;lt;/i&amp;gt;(1) Gauge Field

Recently we have studied the instant-form quantization (IFQ) and the light-front quantization (LFQ) of the conformally gauge-fixed Polyakov D1 brane action using the Hamiltonian and path integral formulations. The IFQ is studied in the equal world-sheet time framework on the hyperplanes defined by the world-sheet time σ0=τ=constant and the LFQ in the equal light-cone world-sheet time framework, on the hyperplanes of the light-front defined by the light-cone world-sheet time σ+= (τ+σ) =constant. The light-front theory is seen to be a constrained system in the sense of Dirac in contrast to the instant-form theory. However, owing to the gauge anomalous nature of these theories, both of these theories are seen to lack the usual string gauge symmetries defined by the world-sheet reparametrization invariance (WSRI) and the Weyl invariance (WI). In the present work we show that these theories when considered in the presence of background gauge fields such as the NSNS 2-form gauge field Bαβ(σ,τ) or in the presence of U(1) gauge field Aα(σ,τ) and the constant scalar axion field C(σ,τ), then they are seen to possess the usual string gauge symmetries (WSRI and WI). In fact, these background gauge fields are seen to behave as the Wess-Zumino or Stueckelberg fields and the terms containing these fields are seen to behave as Wess-Zumino or Stueckelberg terms for these theories.

B-field in AdS 3/CF T 2 correspondence and integrability

We construct topological Wess-Zumino term for supercoset sigma-models on various AdS(3) backgrounds. For appropriately chosen set of parameters, the sigma-model remains integrable when the Wess-Zumino term is added to the action. Moreover, the conditions for integrability, kappa-symmetry and conformal invariance are equivalent to each other.

Supersymmetric domain walls

We classify the half-supersymmetric "domain walls", i.e. branes of codimension one, in toroidally compactified IIA/IIB string theory and show to which gauged supergravity theory each of these domain walls belong. We use as input the requirement of supersymmetric Wess-Zumino terms, the properties of the E11 Kac-Moody algebra and the embedding tensor formalism. We show that the number of half-supersymmetric domain walls is a multiple of the number of corresponding central charges in the supersymmetry algebra, where the multiplicity is related to the degeneracy of the BPS conditions.

Consistent bilinear Wess-Zumino term for open AdS superstring

We consider the open superstring action in AdS5 × S5 background with the bilinear Wess-Zumino term, which has been modified in such a way that a certain total derivative term is absent, and give the covariant description of supersymmetric D-branes. We show that the modification of bilinear Wess-Zumino term is necessary to describe correctly the 1/2-BPS D(-1)-brane in AdS5 × S5 background, while the classification of other supersymmetric D-branes does not depend on such modification.

N = 4 SYM low-energy effective action in N = 4 harmonic superspace

We apply the N = 4 harmonic superspace with USp(4) harmonic variables for describing the N = 4 SYM low-energy effective action. Scale invariance and gauge symmetry fix the leading term in the low-energy effective action uniquely, up to a constant. The value of the remaining constant can be fixed by the topological quantization condition for the Wess-Zumino term which is present in the component structure of this action.

More on closed string induced higher derivative interactions on D-branes

In our continued efforts of matching full string computations with the corresponding effective field theory computations, we evaluate string theory correlators in closed forms. In particular, we consider a correlator between three SYM vertex operators and one Ramond-Ramond $C$-field vertex operator: $<V_{C}V_{\phi} V_AV_A>$. We show that the infinite number of massless poles of this amplitude can be reproduced by the Born-Infeld action, the Wess-Zumino terms, and their higher derivative corrections. More specifically we find, up to an on-shell ambiguity, two scalar field and two gauge field couplings to all orders in $\alpha'$ such that the infinite number of massless poles of the field theory amplitude exactly match the infinite number of massless poles of S-matrix elements of $<V_{C}V_{\phi} V_AV_A>$. We comment on close intertwinedness of an open string and a closed string that must be behind the matching.

Galileons as Wess-Zumino terms

We show that the galileons can be thought of as Wess-Zumino terms for the spontaneous breaking of space-time symmetries. Wess-Zumino terms are terms which are not captured by the coset construction for phenomenological Lagrangians with broken symmetries. Rather they are, in d space-time dimensions, d-form potentials for (d+1)-forms which are non-trivial co-cycles in Lie algebra cohomology of the full symmetry group relative to the unbroken symmetry group. We introduce the galileon algebras and construct the non-trivial (d+1)-form co-cycles, showing that the presence of galileons and multi-galileons in all dimensions is counted by the dimensions of particular Lie algebra cohomology groups. We also discuss the DBI and conformal galileons from this point of view, showing that they are not Wess-Zumino terms, with one exception in each case.

Three form potential in (special) minimal supergravity superspace and supermembrane supercurrent

This contribution begins the study of the complete superfield Lagrangian description of the interacting system of D = 4 \U0001d4a9 = 1 supergravity (SUGRA) and supermembrane. Firstly, we review a 'three form supergravity' by Ovrut and Waldram, which we prefer to call 'special minimal supergravity'. This off-shell formulation of simple SUGRA is appropriate for our purposes as the supermembrane action contains the so–called Wess–Zumino term given by the integral over a three form potential in superspace, C3. We describe this formulation in the frame of Wess–Zumino superfield approach, showing how the basic variations of minimal SUGRA are restricted by the conditions of the existence of a three-form potential C3 in its superspace. In this language the effect of dynamical generation of cosmological constant, known to be characteristic for this formulation of SUGRA, appears in its superfield form, first described by Ogievetsky and Sokatchev in their formulation of SUGRA as a theory of axial vector superfield. Secondly, we vary the supermembrane action with respect to the special minimal SUGRA superfields (basic variations) and obtain the supercurrent superfields as well as the supergravity superfield equations with the supermembrane contributions.

Elliptic Integrable Systems: a Comprehensive Geometric Interpretation

We give a geometric interpretation of all the $m$-th elliptic integrable systems associated to a $k'$-symmetric space $N=G/G_0$ (in the sense of C.L. Terng). It turns out that we have to introduce the integer $m_{k'}$ defined by m_{1}=0 and m_{k'}= [(k'+1)/2]. Then the general problem splits into three cases : the primitive case ($m < m_{k'}$), the determined case ($m_{k'}\leq m \leq k'-1$) and the underdetermined case ($m \geq k'$). We prove that we have an interpretation in terms of a sigma model with a Wess-Zumino term. Moreover we prove that we have a geometric interpretation in terms of twistors. See the abstract in the paper for more precisions.