In the holographic model of QCD, theta dependence sharply changes at the point of confinement deconfinement phase transition. In large N QCD such a change in theta behavior can be related to the breakdown of the instanton expansion at some critical temperature T_c. Associating this temperature with confinement-deconfinement phase transition leads to the description of the latter in terms of dissociation of instantons into the fractionally charged instanton quarks. To elucidate this picture, we introduce the nonvanishing chiral condensate in the deconfining phase and assume a specific lagrangian for the eta' field in the confining phase. In the resulting picture the high temperature phase of the theory consists of the dilute gas of instantons, while the low temperature phase is described in terms of freely moving fractional instanton quarks.
Effects of the theta parameter are studied in Witten's model of holographic 4d Yang-Mills, where theta is the coefficient of the CP-breaking topological term. First, the gravity background, including the full backreaction of the RR form dual to the theta parameter, is revisited. Then, a number of observables are computed holographically: the ground-state energy density, the string tension, the 't Hooft loop, the light scalar glueball mass, the baryon mass scale, the critical temperature for deconfinement - and thus the whole (T, theta) phase diagram - and the entanglement entropy. A simple rul…
Based on the intanton approximation of Skyrmion and recent progresses on the holographic approach, we study baryon properties using Skyrmions generated from holographic instantons. First we employ Atiyah and Manton's early observation to show that the instanton approximation gives the correct infrared behavior for the Skyrmion solution, and thus those of the electromagnetic form factors of the nucleon. We then use Skyrmions generated from flat-space instanton solutions to study various baryon properties, treating the instanton size as an arbitrary variable. It is found that, a large instanton …
V-QCD is a class of effective holographic models for QCD which fully includes the backreaction of quarks to gluon dynamics. The physics of the theta-angle and the axial anomaly can be consistently included in these models. We analyze their phase diagrams over ranges of values of the quark mass, N_f/N_c, and theta, computing observables such as the topological susceptibility and the meson masses. At small quark mass, where effective chiral Lagrangians are reliable, they agree with the predictions of V-QCD.
Small instantons can play an important role in Yang-Mills theories whose gauge couplings are sizeable at small distances. An interesting class of theories where this could occur is in weakly-gauged holographic models (dual to Yang-Mills theories interacting with strongly-coupled CFTs), since gauge couplings are indeed enhanced towards the UV boundary of the 5D AdS space. However, contrary to expectations, we show that small instantons in these non-asymptotically-free models are highly suppressed and ineffective. This is due to the conservation of topological charge that forbids instantons to b…
We formulate a toy model for the $θ$ vacuum that embodies the n-point moments of the even and odd topological charge densities. The partition function is $2π$ periodic only after resumming over all winding modes. We apply the same analysis to the quenched instanton vacuum at finite $θ$ and derive saddle-point results for the vacuum energy density that are manifestly $2π$ periodic whatever $θ$. We briefly discuss the consequences of unquenching the fermions on our results.
We consider aspects of dynamical baryons in a holographic dual of QCD that is proposed on the basis of a D4/D8-brane configuration. We construct a soliton solution carrying a unit baryon number and show that it is given by an instanton solution of four-dimensional Yang-Mills theory with fixed size. The Chern-Simons term on the flavor D8-branes plays a crucial role of protecting the instanton from collapsing to zero size. By quantizing the collective coordinates of the soliton, we work out the baryon spectra. Negative-parity baryons as well as baryons with higher spins and isospins can be obtai…
The theta-dependent gauge theories can be studied by using holographic duality through string theory on certain spacetimes. Via this correspondence we consider a stack of $N_{0}$ dynamical D0-branes as D-instantons in the background sourced by $N_{c}$ coincident non-extreme black D4-branes. According to the gauge-gravity duality this D0-D4 brane system corresponds to Yang-Mills theory with a theta angle at finite temperature. We solve the IIA supergravity action by taking account into a sufficiently small backreaction of the D-instantons and obtain an analytical solution for our D0-D4-brane co…
We investigate the dependence of four-dimensional SU(N) gauge theories on the topological theta term at finite temperature and, in particular, across the deconfinement transition. For this purpose, we exploit the lattice formulation of the theory and present numerical results for the expansion of the free energy up to O(theta^6), for N=3 and N=6. Our numerical analysis shows that the theta dependence of 4D SU(N) gauge theory experiences a drastic change across the deconfinement transition: the low-temperature phase is characterized by a large-N scaling with theta/N as relevant variable, while …
We study meson decays using instanton methods in two string models. The first model is the old string model in flat space which combines strings and massive particles and the second is the holographic, Sakai-Sugimoto model. Using the the old string model, we reproduce the QCD formula for the probability of splitting of the QCD flux tube derived by Casher-Neuberger-Nussinov (CNN). In the holographic model we construct a string worldsheet instanton which interpolates between a single and double string configuration, which determines the decay from one to two dual mesonic particles. The resulting…
We study cold nuclear matter based on the holographic gauge theory, where baryons are introduced as the instantons in the probe D8/D8 branes according to the Sakai-Sugimoto model. Within a dilute gas approximation of instantons, we search for the stable states via the variational method and fix the instanton size. We find the first order phase transition from the vacuum to the nuclear matter phase as we increase the chemical potential. At the critical chemical potential, we could see a jump in the baryon density from zero to a finite definite value. While the size of the baryon in the nuclear …
We discuss homogeneous baryonic matter in the decompactified limit of the Sakai-Sugimoto model, improving existing approximations based on flat-space instantons. We allow for an anisotropic deformation of the instantons in the holographic and spatial directions and for a density-dependent distribution of arbitrarily many instanton layers in the bulk. Within our approximation, the baryon onset turns out to be a second-order phase transition, at odds with nature, and there is no transition to quark matter at high densities, at odds with expectations from QCD. This changes when we impose certain …
We investigate properties of baryons in a family of holographic field theories related to the Sakai-Sugimoto model of holographic QCD. Starting with the $N_f=2$ Sakai-Sugimoto model, we truncate to a 5D Yang-Mills action for the gauge fields associated with the noncompact directions of the flavour D8-branes. We define a free parameter $γ$ that controls the strength of this Yang-Mills term relative to the Chern-Simons term that couples the abelian gauge field to the SU(2) instanton density. Moving away from $γ= 0$ should incorporate some of the effects of taking the Sakai-Sugimoto model away fr…
In a wide class of holographic models, like the one proposed by Sakai and Sugimoto, baryons can be approximated by instantons of non-abelian gauge fields that live on the world-volume of flavor D-branes. In the leading order, those are just the Yang-Mills instantons, whose solutions can be obtained from the celebrated ADHM construction. This fact can be used to study various properties of baryons in the holographic limit. In particular, one can attempt to construct a holographic description of the cold dense nuclear matter phase of baryons. It can be argued that holographic baryons in such a r…
We discuss nuclear matter and the transition to quark matter in the decompactified limit of the Sakai-Sugimoto model. Nuclear matter is included through instantons on the flavor branes of the model. Our approximation is based on the flat-space solution, but we allow for a dynamical instanton width and deformation and compute the energetically preferred number of instanton layers in the bulk as a function of the baryon chemical potential. We determine the regions in parameter space where the binding energy of nuclear matter is like in QCD, and compute the phase diagram in the plane of temperatu…
In this work, we first derive the corrections to the instanton configuration of the flavored gauge field in the D4-D8 model with generic flavor numbers. Then, as the instanton configuration on the D8-branes represents equivalently baryon in this model, keeping our corrections in hand, we systemically study the spectrum of baryon, heavy-light baryon or heavy-light meson and find it is possible to fit the experimental data with the meson data in this model. Besides, we briefly outline how to include the interaction of glueball and heavy-light meson or baryon with our corrections, evaluate numeri…
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}…
Using the gauge-gravity duality, we study the holographic Schwinger effect by performing the potential analysis on the confining D3- and D4-brane background with D-instantons then evaluate the pair production/decay rate by taking account into a fundamental string and a single flavor brane respectively. The two confining backgrounds with D-instantons are obtained from the black D(-1)-D3 and D0-D4 solution with a double Wick rotation. The total potential and pair production/decay rate in the Schwinger effect are calculated numerically by examining the NG action of a fundamental string and the DB…
We use a variant of the $D4$-$D8$ construction that includes two chiral and one heavy meson, to describe heavy-light baryons and their exotics as heavy mesons bound to a flavor instanton in bulk. At strong coupling, the heavy meson is shown to {\it always bind} in the form of a flavor instanton zero mode in the fundamental representation. The ensuing instanton moduli for the heavy baryons exhibits both chiral and heavy quark symmetry. We detail how to quantize it, and derive model independent mass relations for heavy bayons with a single-heavy quark in leading order, in overall agreement with …
This work is devoted to the study of the CP-breaking dynamics in QCD, at finite theta-angle. By working in the semi-classical limit, in which the topology of the vacuum is clustered around instantons and anti-instantons, we show that quantum fluctuations of the theta-vacuum generate an effective flavor-dependent repulsion between matter and anti-matter, inside hadrons. As a consequence, during the tunneling between the degenerate vacua, quarks and anti-quarks in the neutron migrate in opposite directions, giving rise to an oscillating electric dipole moment. We discuss a possible phenomenologi…
In the string holographic dual of large-N_c QCD with N_f flavours of Kruczenski et al, the eta' meson is massless at infinite N_c and dual to a collective fluctuation of N_f D6-brane probes in a supergravity background. Here we identify the string diagrams responsible for the generation of a mass of order N_f/N_c, consistent with the Witten-Veneziano formula, and show that the supregravity limit of these diagrams corresponds to mixings with pseudoscalar glueballs. We argue that the dependence on the theta-angle in the supergravity description occurs only through the combination theta + 2 \sqrt…
Roles of instanton induced interactions (III) in the masses of pentaquark baryons, Theta^+ (J=1/2 and 3/2) and Xi^{--}, and a dibaryon, H, are discussed using the MIT bag model in the negative parity case. It is shown that the two-body terms in III give a strong attraction mainly due to the increase of the number of pairs in multi-quark systems. In contrast, the three-body u-d-s interaction is repulsive. It is found that III lowers the mass of Theta^+ as much as 100 MeV from the mass predicted by the bag model without III.
In the holographic model of QCD suggested by Sakai and Sugimoto, baryons are chiral solitons sourced by D4 instantons in bulk of size 1/\sqrtλ with λ=g^2N_c. We quantize the D4 instanton semiclassically using \hbar=1/(N_cλ) and non-rigid constraints on the vector mesons. The holographic baryon is a small chiral bag in the holographic direction with a Cheshire cat smile. The vector-baryon interactions occur at the core boundary of the instanton in D4. They are strong and of order 1/\sqrt{\hbar}. To order \hbar^0 the electromagnetic current is entirely encoded on the core boundary and vector-mes…
A general class of holographic theories with a nontrivial $θ$-angle are analyzed. The instanton density operator is dual to a bulk axion field. We calculate the ground-state solutions with nontrivial source, $a_{UV}$, for the axion, for both steep and soft dilaton potentials in the IR, and both in $d=3$ and $d=4$. We find all cases to be qualitatively similar. We also calculate the spin$=2,0$ glueball spectra and show that the glueball masses monotonically decrease as functions of $a_{UV}$ (or $θ$-angle). The slopes of glueball masses are different, generically, in different potentials. In the…
Roles of instanton induced interactions (III) in the masses of pentaquark baryons, Theta^+ (J=1/2 and 3/2) and Xi^{--}, and a dibaryon, H, are discussed using the MIT bag model. It is shown that the two-body terms in III give a strong attraction mainly due to the increase of the number of pairs in multi-quark systems. In contrast, the three-body $u$-$d$-$s$ interaction is repulsive. It is found that III lowers the mass of negative-parity Theta^+ as much as 100 MeV from the mass predicted by the bag model without III.
We demonstrate a holographic realization of color-flavor locking phase, using N=4 SU(Nc) SYM coupled to N=2 Nf fundamental hypermultiplets as an example. The gravity dual consists of Nc D3-branes and Nf D7-branes with world volume gauge field representing the baryon density. Treating a small number \tilde{N}c << Nc of D3-branes as Yang-Mills instantons on the D7-branes, we consider possible potential(s) on their moduli space or equivalently the Higgs branch. We show that a non-trivial potential can be generated by including the backreaction of the baryonic density on the D7-branes, this dynami…
We study the Sakai-Sugimoto model of holographic QCD at zero temperature and finite chemical potential. We find that as the baryon chemical potential is increased above a critical value, there is a phase transition to a nuclear matter phase characterized by a condensate of instantons on the probe D-branes in the string theory dual. As a result of electrostatic interactions between the instantons, this condensate expands towards the UV when the chemical potential is increased, giving a holographic version of the expansion of the Fermi surface. We argue based on properties of instantons that the…
We investigate cold dense matter in the context of Sakai and Sugimoto's holographic model of QCD in the Wigner-Seitz approximation. In bulk, baryons are treated as instantons on S^3\times R^1 in each Wigner-Seitz cell. In holographic QCD, Skyrmions are instanton holonomies along the conformal direction. The high density phase is identified with a crystal of holographic Skyrmions with restored chiral symmetry at about 4 Mkk^3/pi^5. As the average density goes up, it approaches to uniform distribution while the chiral condensate approaches to p-wave over a cell. The chiral symmetry is effectivel…
Dense QCD at zero temperature with a large number of colors is a crystal. We show that in the holographic dual description, the crystal is made out of pairs of dyons with $e=g=\pm 1$ charges in a salt-like arrangement. We argue that with increasing density the dyon masses and topological charges equalize, turning the salt-like configuration to a bcc of half-instantons. The latter is dual to a cubic crystal of half-skyrmions. We estimate the transition from an fcc crystal of instantons to a bcc crystal of dyons to about 3 times nuclear matter density with a dyon binding energy of about 180 MeV.
We discuss the baryon in the holographic QCD framework and focus on the role of the bifundamental scalar field, realizing chiral symmetry breaking. We suggest the interpretation of a baryon as a dyonic instanton within the Atiyah-Manton-like approach for the flavor gauge group in the peculiar cylindrical ansatz in five-dimensional theory. Our approach provides the new mechanism of the stabilization of the baryon size.
We investigate instantons in finite temperature QCD via Witten's holographic QCD. To study the deconfinement phase, we use the setup proposed in [1] (arXiv:1107.4048). We find that the sizes of the instantons are stabilized at certain values both in the confinement and deconfinement phases. This agrees with the numerical result in the lattice gauge theory. Besides we find that the gravity duals of the large and small instantons in the deconfinement phase have different topologies. We also argue that the fluctuation of the topological charges is large in confinement phase while it is exponentia…
In this paper we discuss new flavored space-like defects in confined QCD which can be considered as the Euclidean extended instantons carrying the topologically quantized currents. We focus on the simplest 1d space-like defect - the S-Skyrmion solution extended in one space coordinate and localized in Euclidean time. It can be identified both in the holographic QCD and in the Chiral Perturbation Theory(ChPT). The Skyrmion charges get transformed into the corresponding currents for S-Skyrmion. The analogy with the Thouless pump and the quantum phase slip phenomena is mentioned.
We study dense nuclear and quark matter within a single microscopic approach, namely the holographic Sakai-Sugimoto model. Nuclear matter is described via instantons in the bulk, and we show that instanton interactions are crucial for a continuous connection of chirally broken and chirally symmetric phases. The continuous path from nuclear to quark matter includes metastable and unstable stationary points of the potential, while the actual chiral phase transition remains of first order, as in earlier approximations. We show that the model parameters can be chosen to reproduce low-density prope…
Spontaneous CP-violation in the strong interaction is analyzed at theta = pi within the framework of the two-flavor NJL model. It is found that the occurrence of spontaneous CP-violation at theta = pi depends on the strength of the 't Hooft determinant interaction, which describes the effect of instanton interactions. The dependence of the phase structure, and in particular of the CP-violating phase, on the quark masses, temperature, baryon and isospin chemical potential is examined in detail. When available a comparison to earlier results from chiral perturbation theory is made. From our resu…
We discuss the description of baryon as the dyonic instanton in holographic QCD. The solution generalizes the Skyrmion taking into account the infinite tower of vector and axial mesons as well as the chiral condensate. We construct the solution with unit baryon charge and study the dependence of its mass on the chiral condensate. The elegant explanation of the Ioffe's formula has been found and we speculate on the relation between physical scales of the chiral and conformal symmetry breaking.
In the large N limit cold dense nuclear matter must be in a lattice phase. This applies also to holographic models of hadron physics. In a class of such models, like the generalized Sakai-Sugimoto model, baryons take the form of instantons of the effective flavor gauge theory that resides on probe flavor branes. In this paper we study the phase structure of baryonic crystals by analyzing discrete periodic configurations of such instantons. We find that instanton configurations exhibit a series of "popcorn" transitions upon increasing the density. Through these transitions normal (3D) lattices …
We present an analysis of the three-flavor holographic model of QCD associated to a $D4/D8$ brane configuration, with symmetry breaking induced by a worldsheet instanton associated to a closed loop connecting $D4-D8-D6-\overline{D8}$. We calculate the electromagnetic and axial couplings of all octet and decuplet baryons, as well as several negative parity excitations, with and without symmetry breaking effects, and demonstrate qualitative and quantitative agreement with many available experimental measurements, with marked improvement over the analogous two-flavor models.
Using the twisted partition function on R^3 x S^1, we argue that the deconfinement phase transition in pure Yang-Mills theory for all simple gauge groups is continuously connected to a quantum phase transition that can be studied in a controlled way. We explicitly consider two classes of theories, gauge theories with a center symmetry, such as SU(N_c) gauge theory for arbitrary N_c, and theories without a center symmetry, such as G_2 gauge theory. The mechanism governing the phase transition is universal and valid for all simple groups. The perturbative one-loop potential as well as monopole-i…
Nuclear matter at large number of colors is necessarily in a solid phase. In particular holographic nuclear matter takes the form of a crystal of instantons of the flavor group. In this article we initiate the analysis of the three-dimensional crystal structures and the orientation patterns for the two-body potential that follows from holographic duality. The outcome of the analysis includes several unexpected results. We perform simulations of ensembles of O(10000) instantons whereby we identify the lattice structure and orientations for the different values of the weight factors of the non-A…
We compute euclidean coordinate space correlation functions in a holographic model of QCD. We concentrate, in particular, on channels that are related to the U(1)_A problem, the flavor-singlet axialvector, pseudoscalar meson, and pseudoscalar glueball (topological charge) correlator. We find that even a very simple holographic model defined on a slice of AdS_5 provides a qualitatively correct description of QCD correlation functions. We study the role of anomaly terms, and show that both euclidean positivity and low energy theorems based on the axial anomaly relation are correctly implemented.…
We derive and systematically analyze scalar glueball correlation functions in both the hard-wall and dilaton soft-wall approximations to holographic QCD. The dynamical content of the holographic correlators is uncovered by examining their spectral density and by relating them to the operator product expansion, a dilatational low-energy theorem and a recently suggested two-dimensional power correction associated with the short-distance behavior of the heavy-quark potential. This approach provides holographic estimates for the three lowest-dimensional gluon condensates or alternatively their Wil…
This paper is a continuation of ArXiv:0707.1324 where improved holographic theories for QCD were set up and explored. Here, the IR confining geometries are classified and analyzed. They all end in a "good" (repulsive) singularity in the IR. The glueball spectra are gaped and discrete, and they favorably compare to the lattice data. Quite generally, confinement and discrete spectra imply each other. Asymptotically linear glueball masses can also be achieved. Asymptotic mass ratios of various glueballs with different spin also turn out to be universal. Mesons dynamics is implemented via space fi…
We propose several quark mass deformations of the holographic model of massless QCD using the D4/D8/D8bar brane configuration proposed by Sakai and Sugimoto. The deformations are based on introducing additional D4 or D6 branes away from the QCD D4 branes. The idea is similar to extended technicolor theories, where the chiral symmetry breaking by additional D-branes are mediated to QCD to induce non-zero quark masses. In the D-brane picture as well as the holographic dual gravity description, the quark and the pion masses are generated by novel worldsheet instantons with finite area. We also de…
The infinite tower of vector mesons encoded in holographic dual QCD bring drastic changes to the soliton structure of the nucleon. The nucleon is given by a point-like instanton in 5D surrounded by a vector meson cloud with the vector dominance restored by the infinite tower. I discuss the possible relevance of this structure in hot and dense hadronic matter.
As is well-known, spontaneous CP-violation in the strong interaction is possible at theta = pi, which is commonly referred to as Dashen's phenomenon. This phenomenon has been studied extensively using chiral Lagrangians. Here the two-flavor NJL model at theta = pi is discussed. It turns out that the occurrence of spontaneous CP-violation depends on the strength of the 't Hooft determinant interaction, which describes the effect of instanton interactions. The dependence of the phase structure, and in particular of the CP-violating phase, on the quark masses, temperature, baryon and isospin chem…
Single quarks moving in the vacuum of confining gauge theories are stopped by a drag force. The holographic description relates the confining scale in the bulk geometry with a range of physical values for the drag force in the vacuum. The vacuum drag force acting on the isolated quark directly manifests quark confinement since it prevents the quark from walking freely in the vacuum. However, analytical expressions for the drag force as a function of the quark velocity were lacking. In the present work, we propose that the vacuum drag force is given by the regularized zero-temperature limit of …
In this paper we study the dynamical instability of Sakai-Sugimoto's holographic QCD model at finite baryon density. In this model, the baryon density, represented by the smeared instanton on the worldvolume of the probe D8-\overline{D8} mesonic brane, sources the worldvolume electric field, and through the Chern-Simons term it will induces the instability to form a chiral helical wave. This is similar to Deryagin-Grigoriev-Rubakov instability to form the chiral density wave for large N_c QCD at finite density. Our results show that this kind of instability occurs for sufficiently high baryon …
We introduce the strong CP-violation in the framework of AdS/QCD model and calculate the electric dipole moments of nucleons as well as the CP-violating pion-nucleon coupling. Our holographic estimate of the electric dipole moments gives for the neutron d_n=1.08 X 10^{-16} theta (e cm), which is comparable with previous estimates. We also predict that the electric dipole moment of the proton should be precisely the minus of the neutron electric dipole moment, thus leading to a new sum rule on the electric dipole moments of baryons.
We study dynamical baryons in the holographic QCD model of Sakai and Sugimoto in the case of three flavors and with special interest in the construction of the Chern-Simons (CS) term. The baryon classical solution in this model is given by the BPST instanton, and we carry out the collective coordinate quantization of the solution. The CS term should give rise to a first class constraint which selects baryon states with right spins. However, the original CS term written in terms of the CS 5-form does not work. We instead propose a new CS term which is gauge invariant and is given as an integral…
We study topological objects in holographic QCD based on the Sakai-Sugimoto model, which is constructed with $N_c$ D4 branes and $N_f$ D8/$\bar{\rm D8}$ branes in the superstring theory, and is infrared equivalent to 1+3 dimensional massless QCD. Using the gauge/gravity duality, holographic QCD is described as 1+4 dimensional U($N_f$) gauge theory in flavor space with a background gravity, and its instanton solutions correspond to baryons. First, using the Witten Ansatz, we reduce holographic QCD into a 1+2 dimensional Abelian Higgs theory in a curved space and consider its topological aspect.…
We revisit the holographic description of strange baryons in the context of the Sakai-Sugimoto construction, by considering the strange quark mass as heavy. Hyperons are described by a massive $(K,K^*)$ multiplet, bound to a light-flavor instanton in bulk, much in the spirit of the Callan-Klebanov construction. The modular Hamiltonian maps onto the Landau problem, a charged particle in a 2-dimensional external magnetic field, induced by the bulk Chern-Simons interaction, plus spin-orbit coupling. The ensuing holographic hyperon spectrum compares fairly with the empirical one. The holographic s…
