arXiv subjects

Laith H. Haddad

Publications and source records attributed to Laith H. Haddad.

5 recordsLinked to original sources

arXiv2026

Higher-spin composites and emergent AdS$_3$ geometry in the $(1+1)$-dimensional Gross-Neveu model

We study the $(1+1)$-dimensional Gross-Neveu (GN) model with $N$ fermion species and derive from it an emergent AdS$_3$ geometry together with the leading entries of a holographic dictionary. We use a Bargmann-Wigner fusion scheme to generate an infinite tower of higher-spin composite fields from fundamental fermions and study their relative dynamics. A key feature is that the competition between spin-0 (chiral) condensation and spin-1 pairing defines the radial coordinate $z$ of the bulk geometry. Local fluctuations of this ratio measured by a comoving derivative generate the AdS$_3$ line element, and the large-$N$ species sum promotes $z$ from a parameter to a genuine bulk dimension. The $SO(2,2)$ bulk isometry group, whose special conformal generators mix $z$ with the boundary GN coordinates, emerges from local symmetries of the condensates. Our construction admits two dual holographic frames related by the $\mathbb{Z}_2$ exchange of the spin-0 and spin-1 condensates, covering complementary halves of the GN phase diagram. Significantly, projection onto the spin-2 sector reproduces the linearized Einstein-Hilbert action with Newton's constant $G_3 = \ell_\mathrm{AdS}/4πN^2$. We suggest throughout how the string-theoretic sector of the correspondence may emerge.

hep-th↗

arXiv2026

Integrable deformations of the Dirac--sinh-Gordon system

We construct a two-dimensional family of integrable coupled Dirac--scalar field theories in $1+1$ dimensions, parameterized by $(\thz,α)\in[0,π/2]^2$, whose Lax connection takes values in $\slC$ throughout. The family arises as the orbit of the Dirac--sinh-Gordon system under the $U(1)\times U(1)$ maximal torus of $\mathrm{Inn}(\slC)\cong PSL(2,\CC)$: the $\thz$-$U(1)$ rotates the constant phase of the Dirac mass; the $α$-$U(1)$ rotates its field-dependent phase via $β\to|β|\ee^{\imα}$. Integrability throughout the parameter space follows from a single principle: any automorphism of the Lax algebra preserves the zero-curvature condition, since the condition depends only on the Lie bracket of $\slC$.

math-ph↗

arXiv2024

Spin-charge separation for paired Dirac fermions in $(1+1)$ dimensions

We study Dirac fermions at finite density coupled to a complex pairing field assumed to obey scalar field theory with quartic self-repulsion. The bulk of our work develops the mathematics that elucidates the propagation of fermionic excitations in such systems as independent spin (boosts) and charge (fermion number) degrees of freedom. A necessary ingredient is the presence of broken $U(1)$ symmetry in the pairing field and decoupling of its density and phase. In the fermion sector, these elements give rise to an emergent spin-dependent gauge coupling which binds in-vacuum spin and charge into elementary fermions, while driving proliferation of unbound spin and charge for finite condensation in the pairing field. Notably, the onset of spin-charge separation is signaled by $\mathcal{P} \mathcal{T}$-symmetry breaking and decoupling of spin components under Lorentz transformations. Our investigation concludes with two theorems that identify generic features of spin-charge separation in such systems.

math-ph↗

arXiv2019

Superconductivity and quantum phase transitions in dense QCD$_3$

We present a new perspective on thermal and quantum phase transitions (QPT) in $(2+1)$-dimensional quantum chromodynamics based on symmetries, topology, and quantum dynamical structure of the baryon ground state in the large $N_c$ limit for quarks in the two-index antisymmetric representation. The intermediate and high density regimes are modeled through effective four-fermion interactions, which include attractive scalar and diquark terms, with a term to account for vector meson repulsion at high densities. We address beyond-mean-field phenomena by constructing the quantum field theory for fluctuations in internal degrees of freedom of the baryon ground state using a Madelung decomposition. A key QPT occurs at the meson-diquark transition driven by the ratio of baryon chemical potential to quark mass, $μ_B/m$, or to an external applied magnetic field, $μ_B/|eB|$. Properties of the system at ${μ^c_B} \equiv m, |eB|$ stem from diverging quantum fluctuations of a continuous field $γ$ that modulates the spin-space angular positions of baryon potential minima, identified with discrete chiral $\mathbb{Z}_2^σ$, $\mathbb{Z}_2^{LR} \times \mathbb{Z}_2^{LR}$, and $\mathbb{Z}_4^χ$ symmetries for meson, diquark, and asymptotically free regimes. Remarkably, competition between $μ_B$ and $m$ (or $B$), destroys superconductivity via a \emph{quantum} Berezinskii-Kosterlitz-Thouless (BKT) phase transition at ${μ^c_B}$. Moreover, the large $γ$ fluctuations at ${μ^c_B }$ behave as an additional momentum scale, resulting in an effective $(3+1)$d conformal critical theory there. We use these insights to elucidate the nature of \emph{holographic} BKT transitions, from the field theory side, a result which has remained elusive to date. We derive the QCD phase diagram for $μ_B$ above the baryon mass and find good agreement with results obtained by other methods.

hep-th↗

arXiv2015

Quantum Berezinskii-Kosterlitz-Thouless transition in the superconducting phase of (2+1)-dimensional quantum chromodynamics

We study superconductivity in the hadron-quark mixed phase of planar quantum chromodynamics (QCD) within the large $N$ limit of a Gross-Neveu model modified by a repulsive vector term. At high densities, the combination of scalar attraction and repulsive space-like part of the vector interaction squeezes quarks into baryonic composite states, i.e., Dirac fermions with even numbers of bosonic vortices attached. The time-like vector component induces Cooper pairing between these Fermi surface modes. Remarkably, at zero temperature, competition between the quark density and mass destroys superconductivity via a Berezinskii-Kosterlitz-Thouless (BKT) phase transition driven by diverging chiral quantum fluctuations near criticality. Dissolution of logarithmically bound singlet diquarks is catalyzed by in-plane chiral mixing associated with $\mathbb{Z}_2 \otimes \mathbb{Z}_2 \to \mathbb{Z}_2$ chiral symmetry breaking of the Fermi surface into a transverse spin-polarized triplet ground state. We calculate the QCD phase diagram for quark chemical potential above the baryon mass based purely on Fermi surface considerations and find good agreement with results obtained by other methods. We address similarities between our quantum BKT transition and those found using holographic techniques.

hep-th↗