arXiv subjects

Anton Kapustin

Publications and source records attributed to Anton Kapustin.

122 records · Page 7Linked to original sources

arXiv1999

On Mirror Symmetry in Three Dimensional Abelian Gauge Theories

We present an identity relating the partition function of N=4 supersymmetric QED to that of its dual under mirror symmetry. The identity is a generalized Fourier transform. Many known properties of abelian theories can be derived from this formula, including the mirror transforms for more general gauge and matter content. We show that N=3 Chern-Simons QED and N=4 QED with BF-type couplings are conformal field theories with exactly marginal couplings. Mirror symmetry acts on these theories as strong-weak coupling duality. After identifying the mirror of the gauge coupling (sometimes called the ``magnetic coupling'') we construct a theory which is exactly mirror -- at all scales -- to N=4 SQED. We also study vortex-creation operators in the large $N_f$ limit.

hep-th↗

arXiv1999

D_n Quivers From Branes

D-branes can end on orbifold planes if the action of the orbifold group includes (-1)^{F_L}. We consider configurations of D-branes ending on such orbifolds and study the low-energy theory on their worldvolume. We apply our results to gauge theories with eight supercharges in three and four dimensions. We explain how mirror symmetry for N=4 d=3 gauge theories with gauge group Sp(k) and matter in the antisymmetric tensor and fundamental representations follows from S-duality of IIB string theory. We argue that some of these theories have hidden Fayet-Iliopoulos deformations, not visible classically. We also study a class of finite N=2 d=4 theories (so-called D_n quiver theories) and find their exact solution. The integrable model corresponding to the exact solution is a Hitchin system on an orbifold Riemann surface. We also give a simple derivation of the S-duality group of these theories based on their relationship to SO(2n) instantons on R^2\times T^2.

hep-th↗

arXiv1998

New IR Dualities in Supersymmetric Gauge Theory in Three Dimensions

We present nontrivial examples of d=3 gauge theories with sixteen and eight supercharges which are infrared dual at special points in the moduli space. This duality is distinct from mirror symmetry. To demonstrate duality we construct the gauge theories of interest using D2-branes and orientifolds and then consider their lift to M-theory. We also discuss the strong coupling limit of orientifold two-planes and orbifolds of orientifold six-planes.

hep-th↗

arXiv1998

New N=2 superconformal field theories from M/F theory orbifolds

We consider M-theory on (T^2\times R^2)/Z_n with M5 branes wrapped on R^2. One can probe this background with M5 branes wrapped on T^2. The theories on the probes provide many new examples of N=2 field theories without Lagrangian description. All these theories have Coulomb branches, and we find the corresponding Seiberg-Witten curves. The exact solution is encoded in a Hitchin system on an orbifolded torus with punctures. The theories we consider also arise from D3 probes in F-theory on K3\times K3 orbifolds. Interestingly, the relevant F-theory background has frozen Z_n singularities which are analogous to frozen Z_2 singularities in Type I string theory. We use the F-theory description to find supergravity duals of the probe SCFT's in the large N limit and compute the spectrum of relevant and marginal operators. We also explain how the decoupling of U(1) factors is manifested in the supergravity description.

hep-th↗

arXiv1998

Solution of N=2 Gauge Theories via Compactification to Three Dimensions

A number of N=2 gauge theories can be realized by brane configurations in Type IIA string theory. One way of solving them involves lifting the brane configuration to M-theory. In this paper we present an alternative way of analyzing a subclass of these theories (elliptic models). We observe that upon compactification on a circle one can use a version of mirror symmetry to map the original brane configuration into one containing only D-branes. Simultaneously the Coulomb branch of the four-dimensional theory is mapped to the Higgs branch of a five-dimensional theory with three-dimensional impurities. The latter does not receive quantum corrections and can be analyzed exactly. The solution is naturally formulated in terms of an integrable system, which is a version of a Hitchin system on a punctured torus.

hep-th↗

arXiv1998

The Higgs Branch of Impurity Theories

We consider supersymmetric gauge theories with impurities in various dimensions. These systems arise in the study of intersecting branes. Unlike conventional gauge theories, the Higgs branch of an impurity theory can have compact directions. For models with eight supercharges, the Higgs branch is a hyperKahler manifold given by the moduli space of solutions of certain differential equations. These equations are the dimensional reductions of self-duality equations with boundary conditions determined by the impurities. They can also be interpreted as Nahm transforms of self-duality equations on toroidally compactified spaces. We discuss the application of our results to the light-cone formulation of Yang-Mills theories and to the solution of certain N=2 d=4 gauge theories.

hep-th↗

arXiv1998

Singular Monopoles and Supersymmetric Gauge Theories in Three Dimensions

According to the proposal of Hanany and Witten, Coulomb branches of N=4 SU(n) gauge theories in three dimensions are isometric to moduli spaces of BPS monopoles. We generalize this proposal to gauge theories with matter, which allows us to describe the metrics on their spaces of vacua by means of the hyperkähler quotient construction. To check the identification of moduli spaces a comparison is made with field theory predictions. For SU(2) theory with k fundamental hypermultiplets the Coulomb branch is expected to be the D_k ALF gravitational instanton, so our results lead to a construction of such spaces. In the special case of SU(2) theory with four or fewer fundamental hypermultiplets we calculate the complex structures on the moduli spaces and compare them with field-theoretical results. We also discuss some puzzles with brane realizations of three-dimensional N=4 theories.

hep-th↗

arXiv1997

Annihilation of S-wave quarkonia and the measurement of alpha_s

We analyze the relativistic corrections to annihilation rates of S-wave quarkonia within the framework of NRQCD. We show that order v^2 corrections can be expressed in terms of the heavy quark pole mass and the quarkonium mass. The ratio of hadronic to radiative annihilation rates for eta_b and eta_c can therefore be predicted accurately. The contributions of color-octet operators to the hadronic decay rates of spin-triplet quarkonia are shown to be significant, even though they arise at order v^4 in the velocity expansion. We provide a rough estimate of the color-octet contributions and extract the value of alpha_s from the experimental data on Upsilon decays.

hep-ph↗

arXiv1997

Order 1/m_b^3 corrections to B\to X_c\ell\barνdecay and their implication for the measurement of \barΛand λ_1

We compute the order 1/m_b^3 nonperturbative contributions to the inclusive differential B\to X_c\ell\barνdecay rate. They are parametrized by the expectation values of two local and four nonlocal dimension-six operators. We use our results to estimate part of the theoretical uncertainties in the extraction of matrix elements \barΛand λ_1 from the lepton spectrum in the inclusive semileptonic B decay and find them to be very large. We also compute the 1/m_b^3 corrections to the moments of the hadronic invariant mass spectrum in this decay, and combine them with the extracted values of \barΛand λ_1 to put an upper bound on the branching fraction Br(B\to D^{**}\ell\barν).

hep-ph↗

arXiv1996

The Coulomb branch of N=1 supersymmetric gauge theory with adjoint and fundamental matter

We consider N=1 SU(N_c) gauge theory with an adjoint matter field $Φ$, N_f flavors of fundamentals Q and antifundamentals \tQ, and tree-level superpotential of the form $\tQΦ^l Q$. This superpotential is relevant or marginal for $lN_f\leq 2N_c$. The theory has a Coulomb branch which is not lifted by quantum corrections. We find the exact effective gauge coupling on the Coulomb branch in terms of a family of hyperelliptic curves, thus providing a generalization of known results about N=2 SUSY QCD to N=1 context. The Coulomb branch has singular points at which mutually nonlocal dyons become massless. These singularities presumably correspond to new N=1 superconformal fixed points. We discuss them in some detail for N_c=2, N_f=1.

hep-th↗

arXiv1996

Implications of the $B \to X \ell \barν_\ell$ lepton spectrum for heavy quark physics

The shape of the lepton spectrum in inclusive semileptonic $B\to X\,\ell\,\barν_\ell$ decay is sensitive to matrix elements of the heavy quark effective theory, $\barΛ$ and $λ_1$. From CLEO data we extract $\barΛ=0.39\pm0.11\,$GeV and $λ_1=-0.19\pm0.10\,{\rm GeV}^2$, where the uncertainty is the $1σ$ statistical error only. Systematic uncertainties are discussed. These values for $\barΛ$ and $λ_1$ are used to determine $|V_{cb}|$ and the $\overline{\rm MS}$ bottom and charm quark masses. We discuss the theoretical uncertainties related to order $(Λ_{\rm QCD}/m_b)^3$ effects and higher orders in the perturbative expansion.

hep-ph↗

arXiv1996

Perturbative corrections to zero recoil inclusive $B$ decay sum rules

Comparing the result of inserting a complete set of physical states in a time ordered product of $b$ decay currents with the operator product expansion gives a class of zero recoil sum rules. They sum over physical states with excitation energies less than $Δ$, where $Δ$ is much greater than the QCD scale and much less than the heavy charm and bottom quark masses. These sum rules have been used to derive an upper bound on the zero recoil limit of the $B\to D^*$ form-factor, and on the matrix element of the kinetic energy operator between $B$ meson states. Perturbative corrections to the sum rules of order $α_s(Δ) Δ^2/m_{c,b}^2$ have previously been computed. We calculate the corrections of order $α_s(Δ)$ and $α_s^2(Δ) β_0$ keeping all orders in $Δ/m_{c,b}$, and show that these perturbative QCD corrections suppressed by powers of $Δ/m_{c,b}$ significantly weaken the upper bound on the zero recoil $B\to D^*$ form-factor, and also on the kinetic energy operator's matrix element.

hep-ph↗

arXiv1995

Leading logarithms of the $b$ quark mass in inclusive $B\to X_sγ$ decay

Part of the order $α_s$ correction to the inclusive $B\to X_s\,γ$ photon spectrum is enhanced by $\log(m_b^2/m_s^2)$. We discuss its origin and sum the corrections proportional to $[α_s\log(m_b^2/μ^2)]^n$ to all orders. These are the calculable leading logarithms in the parton fragmentation functions of a quark or gluon into a photon. Although the gluon fragmentation into a photon starts only at order $α_s^2$, its contribution is of the same order as the $s$ quark's in the leading log sum. For not too small values of the photon energy, the resummation yields a moderate suppression. In the standard model, the coefficient of the operator whose matrix element gives rise to such terms is small. A measurement of the photon spectrum around $1\,$GeV would provide a theoretically clean determination of $C_8$, the Wilson coefficient of the $b\to s\,g$ operator.

hep-ph↗

arXiv1995

Moments of the photon spectrum in the inclusive $B\to X_sγ$ decay

The moments of the photon spectrum in the inclusive $B\to X_s\,γ$ decay can be calculated to order $α_s$ accuracy at present, without knowing the $α_s$ corrections to the effective Hamiltonian. We discuss the standard model predictions, and how the moments of the photon spectrum are related to certain matrix elements of the heavy quark effective theory. The sensitivity of these moments to new physics is small, and they provide a model-independent determination of the $b$ quark pole mass (at order $α_s$), or equivalently, the matrix elements $\barΛ$ and $λ_1$ of the effective theory.

hep-ph↗