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We construct a supergravity background corresponding to a backreacted D0/D4-brane system. The background is holographically dual to the Venecianno limit of the Berkoos-Douglas matrix model. It is known that the localized D0/D4 system is unstable when the D0-branes are within the D4-branes. To circumvent this difficulty we separate the D4s from the D0s, which are placed at the origin, and restore the symmetry of the combined system by distributing the D4-branes on a spherical shell around the D0-branes. The backreacted solution is first obtained perturbatively in N_f/N_c and displayed analytically to 1st order. A non-perturbative numerical solution is then presented., Comment: 31 pages, 3 figures, references added

We study a holographic gauge theory dual to the D3/D5 intersection. We consider a pure gauge B-field flux through the internal two-sphere wrapped by the probe D5--brane, which corresponds to a non-commutative configuration of adjoint scalars. There is a domain wall separating the theory into regions with different ranks of the adjoint group. At zero temperature the theory is supersymmetric and at finite temperature there is a critical point of a second order phase transition. We study the corresponding critical exponents and find that the second derivatives of the free energy, with respect to the bare mass and the magnetic field, diverge with a critical exponent of -2/3., Comment: Updated to match the published version

We study the maximally supersymmetric plane wave matrix model (the BMN model) at finite temperature, $T$, and locate the high temperature phase boundary in the $(\mu,T)$ plane, where $\mu$ is the mass parameter. We find the first transition, as the system is cooled from high temperatures, is from an approximately $SO(9)$ symmetric phase to one where three matrices expand to form fuzzy spheres. For $\mu > 3.0$ there is a second distinct transition at a lower temperature. The two transitions approach one another at smaller $\mu$ and merge in the vicinity of $\mu=3.0$. The resulting single transition curve then approaches the gauge/gravity prediction as $\mu$ is further decreased. We find a rough estimate of the transition, for all $\mu$, is given by a Pad\'e resummation of the large-$\mu$, 3-loop perturbative, predictions. We find evidence that the transition at small $\mu$ is to an M5-brane phase of the theory., Comment: minor corrections, typos fixed, acknowledgements updated

We test the background geometry of the BFSS model using a D4-brane probe. This proves a sensitive test of the geometry and we find excellent agreement with the D4-brane predictions based on the solution of a membrane corresponding to the D4-brane propagating on this background., Comment: 7 pages, 2 figures, based on a talk, presented by D. O'C. at ISQS 25, 6-10 June, 2017, Prague, Czech Republic; to be published in Journal of Physics: Conference Series

We study the second derivative of the free energy with respect to the fundamental mass (the mass susceptibility) for the Berkooz-Douglas model as a function of temperature and at zero mass. The model is believed to be holographically dual to a D0/D4 intersection. We perform a lattice simulation of the system at finite temperature and find excellent agreement with predictions from the gravity dual., Comment: typos fixed, acknowledgements updated

We study the high temperature series expansion of the Berkooz-Douglas matrix model which describes the D0/D4--brane system. At high temperature the model is weakly coupled and we develop the series to second order. We check our results against the high temperature regime of the bosonic model (without fermions) and find excellent agreement. We track the temperature dependence of the bosonic model and find backreaction of the fundamental fields lifts the zero temperature adjoint mass degeneracy. In the low temperature phase the system is well described by a gaussian model with three masses $m^t_A=1.964 \pm 0.003$, $m^l_A=2.001 \pm 0.003$ and $m_f=1.463 \pm 0.001$, the adjoint longitudional and transverse masses and the mass of the fundamental fields respectively., Comment: 36 pages 11 figures and tables; v2: major revision for clarification, numerical results updated and typos corrected

We compare the bosonic and maximally supersymmetric membrane models. We find that in Hoppe regulated form the bosonic membrane is well approximated by massive Gaussian quantum matrix models. In contrast the similarly regulated supersymmetric membrane, which is equivalent to the BFSS model, has a gravity dual description. We sketch recent progress in checking gauge/gravity duality in this context., Comment: 11 pages and 4 figures. To appear in the Proceedings of the Corfu Summer Institute 2015 "School and Workshops on Elementary Particle Physics and Gravity" 1-27 September 2015 Corfu, Greece

We perform computer simulations of the Berkooz-Douglas (BD) matrix model, holographically dual to the D0/D4-brane intersection. We generate the fundamental condensate versus bare mass curve of the theory both holographically and from simulations of the BD model. Our studies show excellent agreement of the two approaches in the deconfined phase of the theory and significant deviations in the confined phase. We argue the discrepancy in the confined phase is explained by the embedding of the D4-brane which yields stronger $\alpha'$ corrections to the condensate in this phase., Comment: 29 pages, 3 figures, updated to match the published version

We study the maximally supersymmetric BFSS model at finite temperature and its bosonic relative. For the bosonic model in $p+1$ dimensions, we find that it effectively reduces to a system of gauged Gaussian matrix models. The effective model captures the low temperature regime of the model including one of its two phase transitions. The mass becomes $p^{1/3}\lambda^{1/3}$ for large $p$, with $\lambda$ the 'tHooft coupling. Simulations of the bosonic-BFSS model with $p=9$ give $m=(1.965\pm .007)\lambda^{1/3}$, which is also the mass gap of the Hamiltonian. We argue that there is no `sign' problem in the maximally supersymmetric BFSS model and perform detailed simulations of several observables finding excellent agreement with AdS/CFT predictions when $1/\alpha'$ corrections are included., Comment: 23 pages, 11 figures

We construct a novel supergravity background holographically dual to the flavoured N=1 Supersymmetric Yang-Mills theory. We consider flavours of different masses that produce spherical cavities with radii corresponding to the quark masses. The positive beta function blows at some large radial distance corresponding to the Landau pole of the theory. We explore the Wilson loop between two families of light and heavy quarks and observe a screening of the heavy light potential., Comment: 16 pages, 4 figures

We study a quantum system of $p$ commuting matrices and find that such a quantum system requires an explicit curvature dependent potential in its Lagrangian for the system to have a finite energy ground state. In contrast it is possible to avoid such curvature dependence in the Hamiltonian. We study the eigenvalue distribution for such systems in the large matrix size limit. A critical r\^ole is played by $p=4$. For $p\ge4$ the competition between eigenvalue repulsion and the attractive potential forces the eigenvalues to form a sharp spherical shell., Comment: 17 pages

We analyse a $2+1$ dimensional defect field theory on a two sphere in an external magnetic field. The theory is holographically dual to probe D5-branes in global AdS$_5\times S^5$ background. At any finite magnetic field only the confined phase of the theory is realised. There is a first order quantum phase transition, within the confined phase of theory, ending on a quantum critical point of a second order phase transition. We analyse the condensate and magnetisation of theory and construct its phase diagram. We study the critical exponents near the quantum critical point and find that the second derivatives of the free energy, with respect to the bare mass and the magnetic field, diverge with a critical exponent of $-2/3$. Next, we analyse the meson spectrum of the theory and identify a massless mode at the critical point signalling a diverging correlation length of the quantum fluctuations. We find that the derivative of the meson mass with respect to the bare mass also diverges with a critical exponent of $-2/3$. Finally, our studies of the magnetisation uncover a persistent diamagnetic response similar to that in mesoscopic systems, such as quantum dots and nano tubes., Comment: 26 pages, 16 figures, minor corrections, introduction expanded, typos fixed, format improved, updated to much the published version

In the present work, we discuss the phase structure of bilayer and monolayer phases in the (2+1)-dimensional defect field theory whose gravity dual is obtained by embedding D5/anti-D5 probe flavour branes in the singular conifold. We study in detail the embedding equations and compare the free energies of the resulting configurations at non-zero temperature and external magnetic field perpendicular to the defects. Moreover, we analyse the meson spectrum and confirm the stability of the single bilayer solution., Comment: 24 pages, 8 figures

We perform a systematic study of commutative $SO(p)$ invariant matrix models with quadratic and quartic potentials in the large $N$ limit. We find that the physics of these systems depends crucially on the number of matrices with a critical r\^ole played by $p=4$. For $p\leq4$ the system undergoes a phase transition accompanied by a topology change transition. For $p> 4$ the system is always in the topologically non-trivial phase and the eigenvalue distribution is a Dirac delta function spherical shell. We verify our analytic work with Monte Carlo simulations., Comment: 37 pages, 13 figures, minor corrections, updated to match the published version

We propose a new model of flavour chiral symmetry breaking in a (2+1)-dimensional defect gauge theory of strongly coupled fermions by introducing probe D5/anti-D5-flavour branes on the conifold. After working out the flavour brane embeddings at zero temperature, we thoroughly investigate the spectra of small fluctuations on the world volume of the flavour branes (meson spectrum) and conclude that they are free of tachyons. Thus the proposed probe brane embedding is stable. Moreover, we introduce finite temperature and an external magnetic field and study the thermodynamics of the resulting configurations. Namely, we compute the free energies, entropies, heat capacities and magnetisations. The results are used to establish a detailed phase diagram of the model. We find that the effect of magnetic catalysis of chiral symmetry breaking is realised in our model and show that the meson-melting phase transition coincides with the chiral symmetry breaking phase transition. Furthermore, we show that the model is in a diamagnetic phase., Comment: 1+28 pages, 23 figures, PDFTeX, v2: comments and refs. added, version accepted for publication by JHEP

The eigenvalue distribution of Hoppe's two matrix model is investigated in detail as a function of the model's coupling. For small couplings it is a perturbed Wigner semicircle, while for large couplings it is a parabolic distribution which crosses over to a Wigner semicircle for eigenvalues within approximatley an inverse coupling from the boundary of the distribution. The model is approximately commuting at large couplings and we find the joint eigenvalue distribution of the two matrices. We also study a related three matrix model finding the corresponding three dimensional eigenvalue distribution there also. The techniques developed here are more widely applicable to other multi-matrix models., Comment: 24 pages, 6 figures

We construct the gravity dual of N=1 Non-Commutative SYM theory coupled to Nf smeared massless fundamental flavors. Our solution is analytic and non-perturbative. Near the origin the background reduces to the one corresponding to an ordinary SYM theory. At large radial distances, the dilaton diverges signaling the presence of a UV Landau pole. Considering a probe D3-brane we calculate the effective YM coupling and show that it is independent on the parameter of non-commutativity. We calculate the corresponding beta function and show that it remains positive at all energy scales., Comment: 20 pages, minor corrections, updated to match the published version

We investigate the radial extent of the eigenvalue distribution for Yang-Mills type matrix models. We show that, a three matrix Gaussian model with complex Myers coupling, to leading order in strong coupling is described by commuting matrices whose joint eigenvalue distribution is uniform and confined to a ball of radius R=(3Pi/2g)^(1/3). We then study, perturbatively, a 3-component model with a pure commutator action and find a radial extent broadly consistent with numerical simulations., Comment: 25 pages, appendix expanded, presentation improved, updated to match the published version

The phase structure of flavoured N=2 SYM on a three sphere in an external magnetic field is studied. The pairing effect of the magnetic field competes with the dissociating effect of the Casimir free energy, leading to an interesting phase structure of confined and deconfined phases separated by a critical curve of a first order quantum phase transition. At vanishing magnetic field the phase transition is of a third order. For sufficiently strong magnetic field, the only stable phase is the confined phase and magnetic catalysis of chiral symmetry breaking is realized. The meson spectra of the theory exhibit Zeeman splitting and level crossing and feature a finite jump at the phase transition between the confined and deconfined phases. At strong magnetic field the ground state has a massless mode corresponding to the Goldstone boson associated with the spontaneously broken U(1) R-symmetry analogous to the eta' meson in QCD., Comment: 1+28 pages, 16 figures, v3: minor corrections, a problem with the original ansatz addressed, some typos corrected, references added

We study the effects of the temperature and of a magnetic field in the setup of an intersection of D3/D7 branes, where a large number of D7 branes is smeared in the transverse directions to allow for a perturbative solution in a backreaction parameter. The magnetic field sources an anisotropy in the plasma, and we investigate its physical consequences for the thermodynamics and energy loss of particles probing the system. In particular we comment on the stress-energy tensor of the plasma, the propagation of sound in the directions parallel and orthogonal to the magnetic field, the drag force of a quark moving through the medium and jet quenching., Comment: 29 pages + appendices, 5 figures. v2 Version to appear in JHEP, with minor revisions, references added and typos corrected

Within gauge/gravity duality, we construct a backreacted supergravity background dual to SU(Nc) N=4 SYM coupled to Nf massive fundamental flavours in the presence of an external magnetic field. Our solution is perturbative in a parameter that counts the number of the internal flavour loops. The background has a hollow cavity in the bulk of the geometry, where it is similar to the supergravity dual of a non-commutative SYM. The radius of this cavity is related to the dynamically generated mass of the fundamental fields. We apply our construction to study the effect of magnetic catalysis and develop an appropriate renormalization scheme to compute the free energy and the fundamental condensate of the dual gauge theory as a function of the bare mass. While at leading order in the expansion of the perturbative parameter, the free energy and the fundamental condensate agree with the results obtained in the quenched approximation, at next order we show that the effect of magnetic catalysis is enhanced and the contribution to the condensate of the theory from internal fundamental loops runs logarithmically with the finite cutoff Lambda_UV., Comment: 40 pages, 5 figures

We propose a string dual to the SU(Nc) N=4 SYM coupled to Nf massless fundamental flavors in an external magnetic field. The flavors are introduced by homogeneously smeared Nf D7-branes and the external magnetic field via a non-trivial Kalb-Ramond B-field. Our solution is perturbative in a parameter that counts the number of internal flavor loops. In the limit of vanishing B-field the background reduces to the supersymmetric one obtained in hep-th/0612118. We introduce an additional probe D7--brane and in the supersymmetric limit of vanishing B-field perform a holographic renormalization of its "on-shell" action. We consider also non-supersymmetric probes with fixed worldvolume gauge field corresponding to a magnetic field coupled only to the fundamental fields of the probe brane. We study the influence of the backreacted flavors on the effect of dynamical mass generation. Qualitatively the physical picture remains unchanged. In the next step we consider the case when the magnetic field couples to both the backreacted and the probe fundamental degrees of freedom. At sufficiently strong magnetic field the meson spectrum signals an instability of the probe D7-brane, which we interpret as reflecting an instability of the supergravity background., Comment: 33 pages, 5 figures, v2: minor corrections and references added

We review a recent investigation of the effect of magnetic catalysis of mass generation in holographic Yang-Mills theories. We aim at a self-contained and pedagogical form of the review. We provide a brief field theory background and review the basics of holographic flavordynamics. The main part of the review investigates the influence of external magnetic field on holographic gauge theories dual to the D3/D5-- and D3/D7-- brane intersections. Among the observed phenomena are the spontaneous breaking of a global internal symmetry, Zeeman splitting of the energy levels and the existence of pseudo Goldstone modes. An analytic derivation of the Gell-Mann--Oaks--Renner relation for the D3/D7 set up is reviewed. In the D3/D5 case the pseudo Goldstone modes satisfy non-relativistic dispersion relation. The studies reviewed confirm the universal nature of the magnetic catalysis of mass generation., Comment: 49 pages, 11 figures, a review article

In this paper we investigate the influence of an external magnetic field on a flavoured holographic gauge theory dual to the D3/D5 intersection at finite temperature. Our study shows that the external magnetic field has a freezing effect on the confinement/ deconfinement phase transition. We construct the corresponding phase diagram. We investigate some thermodynamic quantities of the theory. A study of the entropy reveals enhanced relative jump of the entropy at the "chiral" phase transition. A study of the magnetization shows that both the confined and deconfined phases exhibit diamagnetic response. The diamagnetic response in the deconfined phase has a stronger temperature dependence reflecting the temperature dependence of the conductivity. We study the meson spectrum of the theory and analyze the stability of the different phases looking at both normal and quasi-normal semi-classical excitations. For the symmetry breaking phase we analyze the corresponding pseudo-Goldstone modes and prove that they satisfy non-relativistic dispersion relation., Comment: 42 pages, 14 figures

In this work we further extend the investigation of holographic gauge theories in external magnetic fields, continuing earlier work. We study the phenomenon of magnetic catalysis of mass generation in 1+3 and 1+2 dimensions, using D3/D7- and D3/D5-brane systems, respectively. We obtain the low energy effective actions of the corresponding pseudo Goldstone bosons and study their dispersion relations. The D3/D7 system exhibits the usual Gell-Mann--Oakes--Renner (GMOR) relation and a relativistic dispersion relation, while the D3/D5 system exhibits a quadratic non-relativistic dispersion relation and a modified linear GMOR relation. The low energy effective action of the D3/D5 system is related to that describing magnon excitations in a ferromagnet. We also study properties of general Dp/Dq systems in an external magnetic field and verify the universality of the magnetic catalysis of dynamical symmetry breaking., Comment: 41 pages, 11 figures, references added

This thesis is dedicated to the holographic study of flavor dynamics. The technique employed is a D7-brane probing of various D3-brane backgrounds. The first topic covered studies the influence of an external magnetic field on a flavored large N Yang-Mills theory. The theory exhibits spontaneous chiral symmetry breaking. The meson spectrum exhibits Zeeman splitting and characteristic GMOR relation. The second topic examines thermal properties of the dual gauge theory. The third topic studies the phase structure of the finite temperature dual gauge theory in the presence of magnetic field. A phase diagram of the theory is obtained and the meson spectrum is explored. The fourth topic studies the addition of an external electric field. The observed effect is dissociation of the bound quarks, favoring the meson melting, the dissociation of mesons corresponds to an insulator/conductor phase transition. The fifth topic studies the addition of an R-charge chemical potential via brane probing of the spinning D3-brane geometry. The corresponding phase diagram is obtained. The chemical potential favors the dissociation of mesons. The last topic explores universal properties of gauge theories dual to the Dp/Dq system. A universal discrete self-similar behavior associated to the insulator/conductor phase transition is observed and the corresponding scaling exponents are computed., Comment: 226 pages, 59 figures, Ph.D thesis, reference format changed

We show how two important types of phase transition in large N_c gauge theory with fundamental flavours can be cast into the same classifying framework as the meson-melting phase transition. These are quantum fluctuation induced transitions in the presence of an external electric field, or a chemical potential for R-charge. The classifying framework involves the study of the local geometry of a special D-brane embedding, which seeds a self-similar spiral structure in the space of embeddings. The properties of this spiral, characterized by a pair of numbers, capture some key universal features of the transition. Computing these numbers for these non-thermal cases, we find that these transitions are in the same universality class as each other, but have different universal features from the thermal case. We present a natural generalization that yields new universality classes that may pertain to other types of transition., Comment: 22 pages, 4 figures, pdfLaTeX

We consider a D7-brane probe of $AdS_{5}\times S^5$ in the presence of pure gauge $B$-field. The dual gauge theory is flavored Yang-Mills theory in external magnetic field. We explore the dependence of the fermionic condensate on the bare quark mass $m_{q}$ and study the discrete self-similar behavior of the theory near the origin of the parametric space. We calculate the critical exponents of the bare quark mass and the fermionic condensate. A study of the meson spectrum supports the expectation based on thermodynamic considerations that at zero bare quark mass the stable phase of the theory is a chiral symmetry breaking one. Our study reveals the self-similar structure of the spectrum near the critical phase of the theory, characterized by zero fermionic condensate and we calculate the corresponding critical exponent of the meson spectrum., Comment: 29 pages, 9 figures. Accepted in JHEP. Updated to mach the published version. One figure added, some definitions improved

We consider a D7-brane probe of AdS$_{5}\times S^5$ in the presence of pure gauge $B$-field. In the dual gauge theory, the $B$-field couples to the fundamental matter introduced by the D7-brane and acts as an external magnetic field. The $B$-field supports a 6-form Ramond-Ramond potential on the D7-branes world volume that breaks the supersymmetry and enables the dual gauge theory to develop a non-zero fermionic condensate. We explore the dependence of the fermionic condensate on the bare quark mass $m_{q}$ and show that at zero bare quark mass a chiral symmetry is spontaneously broken. A study of the meson spectrum reveals a coupling between the vector and scalar modes, and in the limit of weak magnetic field we observe Zeeman splitting of the states. We also observe the characteristic $\sqrt{m_{q}}$ dependence of the ground state corresponding to the Goldstone boson of spontaneously broken chiral symmetry., Comment: 22 pages, 7 figures, references added, few typos corrected