arXiv subjects

Z. Guralnik

Publications and source records attributed to Z. Guralnik.

18 recordsLinked to original sources

arXiv2013

Complex Path Integrals and the Space of Theories

The Feynman Path Integral is extended in order to capture all solutions of a quantum field theory. This is done via a choice of appropriate integration cycles, parametrized by M in SL(2,C), i.e., the space of allowed integration cycles is related to certain Dp-branes and their properties, which can be further understood in terms of the "physical states" of another theory. We also look into representations of the Feynman Path Integral in terms of a Mellin-Barnes transform, bringing the singularity structure of the theory to the foreground. This implies that, as a sum over paths, we should consider more generic paths than just Brownian ones. Finally, we are able to study the Space of Theories through our examples in terms of their Quantum Phases and associated Stokes' Phenomena (wall-crossing).

hep-th↗

arXiv2006

Calibrated Surfaces and Supersymmetric Wilson Loops

We study the dual gravity description of supersymmetric Wilson loops whose expectation value is unity. They are described by calibrated surfaces that end on the boundary of anti de-Sitter space and are pseudo-holomorphic with respect to an almost complex structure on an eight-dimensional slice of AdS_5 x S^5. The regularized area of these surfaces vanishes, in agreement with field theory non-renormalization theorems for the corresponding operators.

hep-th↗

arXiv2005

Spectral Flow on the Higgs Branch and AdS/CFT Duality

We use AdS/CFT duality to study the large N_c limit of the meson spectrum on the Higgs branch of a strongly coupled, N=2 supersymmetric SU(N_c) gauge theory with N_f =2 fundamental hypermultiplets. In the dual supergravity description, the Higgs branch is described by SU(2) instanton configurations on D7-branes in an AdS background. We compute the spectral flow parameterized by the size of a single instanton. In the large N_c limit, there is a sense in which the flow from zero to infinite instanton size, or Higgs VEV, can be viewed as a closed loop. We show that this flow leads to a non-trivial rearrangement of the spectrum.

hep-th↗

arXiv2004

Less is More: Non-renormalization Theorems from Lower Dimensional Superspace

We discuss a new class of non-renormalization theorems in N=4 and N=2 Super-Yang-Mills theory, obtained by using a superspace which makes a lower dimensional subgroup of the full supersymmetry manifest. Certain Wilson loops (and Wilson lines) belong to the chiral ring of the lower dimensional supersymmetry algebra, and their expectation values can be computed exactly.

hep-th↗

arXiv2003

A Gravity Dual of Chiral Symmetry Breaking

We establish a holographic description of chiral symmetry breaking for a particular confining large N non-supersymmetric gauge theory with matter in the fundamental representation. The gravity dual of this theory is obtained by introducing a D7-brane probe into a deformed Anti-de Sitter background found by Constable and Myers. We numerically compute the \barψψcondensate and meson spectrum by solving the equation of motion of the D7-brane probe in this background. We find a symmetry breaking condensate as well as the associated, pion-like, Goldstone boson in the limit of small quark mass. The existence of the condensate ensures that the D7-brane never reaches the naked singularity at the origin of the deformed AdS space.

hep-th↗

arXiv2003

Chiral Symmetry Breaking and Pions in Non-Supersymmetric Gauge/Gravity Duals

We study gravity duals of large N non-supersymmetric gauge theories with matter in the fundamental representation by introducing a D7-brane probe into deformed AdS backgrounds. In particular, we consider a D7-brane probe in both the AdS Schwarzschild black hole solution and in the background found by Constable and Myers, which involves a non-constant dilaton and S^5 radius. Both these backgrounds exhibit confinement of fundamental matter and a discrete glueball and meson spectrum. We numerically compute the quark condensate and meson spectrum associated with these backgrounds. In the AdS-black hole background, a quark-bilinear condensate develops only at non-zero quark mass. We speculate on the existence of a third order phase transition at a critical quark mass where the D7 embedding undergoes a geometric transition. In the Constable-Myers background, we find a chiral symmetry breaking condensate as well as the associated Goldstone boson in the limit of small quark mass. The existence of the condensate ensures that the D7-brane never reaches the naked singularity at the origin of the deformed AdS space.

hep-th↗

arXiv2003

Properties of Chiral Wilson Loops

We study a class of Wilson Loops in N =4, D=4 Yang-Mills theory belonging to the chiral ring of a N=2, d=1 subalgebra. We show that the expectation value of these loops is independent of their shape. Using properties of the chiral ring, we also show that the expectation value is identically 1. We find the same result for chiral loops in maximally supersymmetric Yang-Mills theory in three, five and six dimensions. In seven dimensions, a generalized Konishi anomaly gives an equation for chiral loops which closely resembles the loop equations of the three dimensional Chern-Simons theory.

hep-th↗

arXiv2002

(De)constructing Intersecting M5-branes

We describe intersecting M5-branes, as well as M5-branes wrapping the holomorphic curve xy=c, in terms of a limit of a defect conformal field theory with two-dimensional (4,0) supersymmetry. This dCFT describes the low-energy theory of intersecting D3-branes at a C^2/Z_k orbifold. In an appropriate k -> infinity limit, two compact spatial directions are generated. By identifying moduli of the M5-M5 intersection in terms of those of the dCFT, we argue that the SU(2)_L R-symmetry of the (4,0) defect CFT matches the SU(2) R-symmetry of the N =2, d=4 theory of the M5-M5 intersection. We find a 't Hooft anomaly in the SU(2)_L R-symmetry, suggesting that tensionless strings give rise to an anomaly in the SU(2) R-symmetry of intersecting M5-branes.

hep-th↗

arXiv2002

Perturbative Instabilities on the Non-Commutative Torus, Morita Duality and Twisted Boundary Conditions

We study one-loop corrections in scalar and gauge field theories on the non-commutative torus. For rational theta, Morita equivalence allows these theories to be reformulated in terms of ordinary theories on a commutative torus with twisted boundary conditions. UV/IR mixing does not lead to singularities, however there can be large corrections. In particular, gauge theories show tachyonic instabilities for some of the modes. We discuss their relevance to spontaneous Z_N x Z_N symmetry breaking in the Morita dual SU(N) theory due to electric flux condensation.

hep-th↗

arXiv2001

Strong Coupling Phenomena on the Noncommutative Plane

We study strong coupling phenomena in U(1) gauge theory on the non-commutative plane. To do so, we make use of a T-dual description in terms of an $N\to\infty$ limit of U(N) gauge theory on a commutative torus. The magnetic flux on this torus is taken to be $m=N-1$, while the area scales like 1/N, keeping $Λ_{QCD}$ fixed. With a few assumptions, we argue that the speed of high frequency light in pure non-commutative QED is modified in the non-commutative directions by the factor $1 + Λ_{QCD}^4 θ^2$, where $θ$ is the non-commutative parameter. If charged flavours are included, there is an upper bound on the momentum of a photon propagating in the non-commutative directions, beyond which it is unstable against production of charged pairs. We also discuss a particular $θ\to\infty$ limit of pure non-commutative QED which is T-dual to a more conventional $N\to\infty$ limit with $m/N$ fixed. In the non-commutative description, this limit gives rise to an exotic theory of open strings.

hep-th↗

arXiv2001

Testing Non-commutative QED, Constructing Non-commutative MHD

The effect of non-commutativity on electromagnetic waves violates Lorentz invariance: in the presence of a background magnetic induction field b, the velocity for propagation transverse to b differs from c, while propagation along b is unchanged. In principle, this allows a test by the Michelson-Morley interference method. We also study non-commutativity in another context, by constructing the theory describing a charged fluid in a strong magnetic field, which forces the fluid particles into their lowest Landau level and renders the fluid dynamics non-commutative, with a Moyal product determined by the background magnetic field.

hep-th↗

arXiv2000

On the Polarization of Unstable D0-Branes into Non-Commutative Odd Spheres

We consider the polarization of unstable type IIB D0-branes in the presence of a background five-form field strength. This phenomenon is studied from the point of view of the leading terms in the non-abelian Born Infeld action of the unstable D0-branes. The equations have SO(4) invariant solutions describing a non-commutative 3-sphere, which becomes a classical 3-sphere in the large N limit. We discuss the interpretation of these solutions as spherical D3-branes. The tachyon plays a tantalizingly geometrical role in relating the fuzzy S^3 geometry to that of a fuzzy S^4.

hep-th↗

arXiv1999

Strings and Discrete Fluxes of QCD

We study discrete fluxes in four dimensional SU(N) gauge theories with a mass gap by using brane compactifications which give ${\cal{N}} = 1$ or ${\cal{N}} = 0$ supersymmetry. We show that when such theories are compactified further on a torus, the t'Hooft magnetic flux $m$ is related to the NS two-form modulus $B$ by $B = 2π{m\over N}$. These values of $B$ label degenerate brane vacua, giving a simple demonstration of magnetic screening. Furthermore, for these values of $B$ one has a conventional gauge theory on a commutative torus, without having to perform any T-dualities. Because of the mass gap, a generic $B$ does not give a four dimensional gauge theory on a non-commutative torus. The Kaluza-Klein modes which must be integrated out to give a four dimensional theory decouple only when $B=2π{m\over N}$. Finally we show that $2π{m\over N}$ behaves like a two form modulus of the QCD string. This confirms a previous conjecture based on properties of large $N$ QCD suggesting a T-duality invariance.

hep-th↗

arXiv1998

Duality of large N Yang-Mills Theory on $T^2 \times R^n$

We find aspects of electrically confining large $N$ Yang-Mills theories on $T^2 \times R^{d-2}$ which are consistent with a $GL(2,Z)$ duality. The modular parameter associated with this $GL(2,Z)$ is given by ${m\over N} + iΛ^2 A$, where $A$ is the area of the torus, $m$ is the t'Hooft twist on the torus, and $Λ^2$ is the string tension. $N$ is taken to infinity keeping $m\over N$ and $g^2N$ fixed. This duality may be interpreted as T-duality of the QCD string if one identifies the magnetic flux with a two-form background in the string theory. Our arguments make no use of supersymmetry. While we are not able to show that this is an exact self duality of conventional QCD, we conjecture that it may be applicable within the universality class of QCD. We discuss the status of the conjecture for the soluble case of pure two dimensional Euclidean QCD on $T^2$, which is almost but not exactly self dual. For higher dimensional theories, we discuss qualitative features consistent with duality. For $m=0$, such a duality would lead to an equivalence between pure QCD on $R^4$ and QCD on $R^2$ with two adjoint scalars. When $Λ^2 A << m^2/N^2$, the proposed duality includes exchanges of rank with twist. This exchange bears some resemblance, but is not equivalent, to Nahm duality. A proposal for an explicit perturbative map which implements duality in this limit is discussed.

hep-th↗

arXiv1997

From 0-Branes to Torons

The moduli space of 0-branes on $T^4$ gives a prediction for the moduli space of torons in U(n) Super Yang Mills theory which preserve 16 supersymmetries. The zero brane number corresponds to the greatest common denominator of the rank $n$, magnetic fluxes and the instanton number. This prediction is derived using U-duality. We explicitly check this prediction by analyzing U(n) bundles with non-zero first as well as second Chern classes. The argument is extended to deduce the moduli space of torons which preserve 8 supersymmetries. Parts of the discussion extend naturally to $T^2$ and $T^3$. Some of the U-dualities involved are related to Lorentz boosts along the eleventh direction in M theory.

hep-th↗

arXiv1997

Torons and D-Brane Bound States

We interpret instantons on a torus with twisted boundary conditions, in terms of bound states of branes. The interplay between the SU(N) and U(1) parts of the U(N) theory of N 4-branes allows the construction of a variety of bound states. The SU(N) and U(1) parts can contribute fractional amounts to the total instanton number which is integral. The geometry of non-self intersecting two-cycles in $T^4$ sheds some light on a number of properties of these solutions.

hep-th↗

arXiv1996

Theta Vacua and Boundary Conditions of the Schwinger Dyson Equations

Quantum field theories and Matrix models have a far richer solution set than is normally considered, due to the many boundary conditions which must be set to specify a solution of the Schwinger-Dyson equations. The complete set of solutions of these equations is obtained by generalizing the path integral to include sums over various inequivalent contours of integration in the complex plane. We discuss the importance of these exotic solutions. While naively the complex contours seem perverse, they are relevant to the study of theta vacua and critical phenomena. Furthermore, it can be shown that within certain phases of many theories, the physical vacuum does not correspond to an integration over a real contour. We discuss the solution set for the special case of one component zero dimensional scalar field theories, and make remarks about matrix models and higher dimensional field theories that will be developed in more detail elsewhere. Even the zero dimensional examples have much structure, and show some analogues of phenomena which are usually attributed to the effects of taking a thermodynamic limit.

hep-th↗

arXiv1994

Strong Corrections to Inclusive B to X tau nu Decays

We calculate the $α_s$ corrections to the form factors which parameterize the hadronic tensor relevant for inclusive semileptonic $B \rightarrow X τ\barν_τ$ and $Λ_b \rightarrow X τ\barν_τ$ decays. We apply our results to the double differential decay rates for the decays of $B$ mesons and polarized $Λ_b$ baryons to polarized $τ$ leptons, presenting them in terms of one-dimensional integrals. Formulas appropriate for insertion into a Monte-Carlo simulation are presented.

hep-ph↗