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Three-dimensional gauge theories coupled to fermions can develop interesting nonperturbative dynamics. Here we study in detail the dynamics of SU(N) gauge theories coupled to a Dirac fermion in the rank-two symmetric and antisymmetric representation. We argue that when the Chern-Simons level is sufficiently small the theory develops a quantum phase with an emergent topological field theory. When the Chern-Simons level vanishes, we further argue that a baryon condenses and hence baryon symmetry is spontaneously broken. The infrared theory then consists of a Nambu-Goldstone boson coupled to a topological field theory. Our proposals also lead to new fermion-fermion dualities involving fermions in two-index representations. We make contact between our proposals and some recently discussed aspects of four-dimensional gauge theories. This leads us to a proposal for the domain wall theories of non-supersymmetric gauge theories with fermions in two-index representations. Finally, we discuss some aspects of the time-reversal anomaly in theories with a one-form symmetry. [ABSTRACT FROM AUTHOR]

We study the finite part of the sphere partition function of d-dimensional Conformal Field Theories (CFTs) as a function of exactly marginal couplings. In odd dimensions, this quantity is physical and independent of the exactly marginal couplings. In even dimensions, this object is generally regularization scheme dependent and thus unphysical. However, in the presence of additional symmetries, the partition function of even-dimensional CFTs can become physical. For two-dimensional $$ \mathcal{N}=\left(2,2\right) $$ supersymmetric CFTs, the continuum partition function exists and computes the Kähler potential on the chiral and twisted chiral superconformal manifolds. We provide a new elementary proof of this result using Ward identities on the sphere. The Kähler transformation ambiguity is identified with a local term in the corresponding $$ \mathcal{N}=\left(2,2\right) $$ supergravity theory. We derive an analogous, new, result in the case of four-dimensional $$ \mathcal{N}=2 $$ supersymmetric CFTs: the S partition function computes the Kähler potential on the superconformal manifold. Finally, we show that $$ \mathcal{N}=1 $$ supersymmetry in four dimensions and $$ \mathcal{N}=\left(1,1\right) $$ supersymmetry in two dimensions are not sufficient to make the corresponding sphere partition functions well-defined functions of the exactly marginal parameters. [ABSTRACT FROM AUTHOR]

We construct the type-IIB AdS4 K supergravity solutions which are dual to the three-dimensional N=4 superconformal field theories that arise as infrared fixed points of circular-quiver gauge theories. These superconformal field theories are labeled by a triple (ρ,...,L) subject to constraints, where ρ and ... are two partitions of a number N, and L is a positive integer. We show that in the limit of large L the localized five-branes in our solutions are effectively smeared, and these type-IIB solutions are dual to the near-horizon geometry of M-theory M2-branes at a C4/(ZkZǩ) orbifold singularity. Our IIB solutions resolve the singularity into localized five-brane throats, without breaking the conformal symmetry. The constraints satisfied by the triple (ρ,...,L), together with the enhanced non-abelian flavour symmetries of the superconformal field theories, are precisely reproduced by the supergravity solutions. As a bonus, we uncover a novel type of "orbifold equivalence" between different quantum field theories and provide quantitative evidence for this equivalence. [ABSTRACT FROM AUTHOR]

We study open and closed string interactions in the type IIB plane wave background using open+closed string field theory. We reproduce all string amplitudes from the dual N=2 Sp(N) gauge theory by computing matrix elements of the dilatation operator. A direct diagrammatic correspondence is found between string theory and gauge theory Feynman diagrams. The prefactor and Neumann matrices of open+closed string field theory are separately realized in terms of gauge theory quantities. [Copyright &y& Elsevier]

We study string interactions among string states with arbitrary impurities in the type IIB plane wave background using string field theory. We reproduce all string amplitudes from gauge theory by computing matrix elements of the dilatation operator in a previously proposed basis of states. A direct correspondence is found between the string field theory and gauge theory Feynman diagrams. [Copyright &y& Elsevier]

We compute string field theory Hamiltonian matrix elements and compare them with matrix elements of the dilatation operator in gauge theory. We get precise agreement between the string field theory and gauge theory computations once the correct cubic Hamiltonian matrix elements in string field theory and a particular basis of states in gauge theory are used. We proceed to compute the matrix elements of the dilatation operator to order g22 in this same basis. This calculation makes a prediction for string field theory Hamiltonian matrix elements to order g22, which have not yet been computed. However, our gauge theory results precisely match the results of the recent computation by Pearson et al. of the order g22 Hamiltonian matrix elements of the string bit model. [Copyright &y& Elsevier]

We find a Penrose limit of AdS5×T1,1 which gives the pp-wave geometry identical to the one that appears in the Penrose limit of AdS5×S5. This leads us to conjecture that there is a subsector of the corresponding N=1 gauge theory which has enhanced N=4 supersymmetry. We identify operators in the N=1 gauge theory with stringy excitations in the pp-wave geometry and discuss how the gauge theory operators fall into N=4 supersymmetry multiplets. We find similar enhancement of symmetry in some other models, but there are also examples in which there is no supersymmetry enhancement in the Penrose limit. [Copyright &y& Elsevier]

We find regular string duals of three-dimensional N=1 SYM with a Chern–Simons interaction at level k for SO and Sp gauge groups. Using the string dual we exactly reproduce the conjectured pattern of supersymmetry breaking proposed by Witten by showing that there is dynamical supersymmetry breaking for k while supersymmetry remains unbroken for k⩾h/2, where h is the dual Coxeter number of the gauge group. We also find regular string duals of four-dimensional N=1 SYM for SO and Sp gauge groups and exactly reproduce the expected pattern of chiral symmetry breaking Z2h→Z2 by analyzing the symmetries of the string solution. [Copyright &y& Elsevier]

We study S-duality in 풩 = 4 super Yang-Mills with an arbitrary gauge group by determining the operator product expansion of the circular BPS Wilson and 't Hooft loop operators. The coefficients in the expansion of an 't Hooft loop operator for chiral primary operators and the stress-energy tensor are calculated in perturbation theory using the quantum path-integral definition of the 't Hooft operator recently proposed. The corresponding operator product coefficients for the dual Wilson loop operator are determined in the strong coupling expansion. The results for the 't Hooft operator in the weak coupling expansion exactly reproduce those for the dual Wilson loop operator in the strong coupling expansion, thereby demonstrating the quantitative prediction of S-duality for these observables. [ABSTRACT FROM AUTHOR]

We lift the bosonic AdS4 × CP3 solution of type IIA supergravity preserving 24 supersymmetries to a D = 10 superspace which has 32 Grassmann-odd directions. The type IIA superspace is obtained from D = 11 via dimensional reduction of the coset superspace OSp(8|4)/SO(7) × SO(1,3) by realizing the latter as a Hopf fibration over the former. This construction generalizes to superspace the Hopf fibration of S7 as a U(1) bundle over CP3, and is suitable for writing the explicit form of Green-Schwarz-type actions encoding the dynamics of the type IIA string and branes in the AdS4 × CP3 superbackground. We show that the OSp(6|4)/U(3) × SO(1,3) supercoset string action describes only a subsector of the complete Green-Schwarz superstring. Thus, even though the superstring equations of motion in the OSp(6|4)/U(3) × SO(1,3) subsector are classically integrable, the fact that the full AdS4 × CP3 superspace is not a supercoset requires the use of more general methods to determine whether the superstring in the complete AdS4 × CP3 superbackground is classically integrable. [ABSTRACT FROM AUTHOR]

We construct vortex loop operators in the three-dimensional 풩 = 6 supersymmetric Chern-Simons theory recently constructed by Aharony, Bergman, Jafferis and Maldacena. These disorder loop operators are specified by a vortex-like singularity for the scalar and gauge fields along a one dimensional curve in spacetime. We identify the 1/2, 1/3 and 1/6 BPS loop operators in the Chern-Simons theory with excitations of M-theory corresponding to M2-branes ending along a curve on the boundary of AdS4 × S7/ℤk. The vortex loop operators can also be given a purely geometric description in terms of regular ``bubbling'' solutions of eleven dimensional supergravity which are asymptotically AdS4 × S7/ℤk. [ABSTRACT FROM AUTHOR]

We find a new sector of string theory in AdS5 × S5 describing non-relativistic superstrings in that geometry. The worldsheet theory of non-relativistic strings in AdS5 × S5 is derived and shown to reduce to a supersymmetric free field theory in AdS2. Non-relativistic string theory provides a new calculable setting in which to study holography. [ABSTRACT FROM AUTHOR]

The effect of fluxes on open string moduli is studied by analyzing the constraints imposed by supersymmetry on D-branes in type IIB flux backgrounds. We show that generically the conditions of supersymmetry cannot be maintained when moving along the geometrical moduli space of the brane, so that open string moduli are lifted. We argue that there is a disconnected and discrete set of supersymmetric solutions to the open string equations of motion, which extends the familiar closed string landscape to the open string sector. [ABSTRACT FROM AUTHOR]

We construct new two dimensional unoriented superstring theories in two dimensions with a chiral closed string spectrum and show that anomalies cancel upon supplying the appropriate chiral open string degrees of freedom imposed by tadpole cancellation. [ABSTRACT FROM AUTHOR]

We construct a Galilean invariant nongravitational closed string theory whose excitations satisfy a nonrelativistic dispersion relation. This theory can be obtained by taking a consistent low energy limit of any of the conventional string theories, including the heterotic string. We give a finite first order worldsheet Hamiltonian for this theory and show that this string theory has a sensible perturbative expansion, interesting high energy behavior of scattering amplitudes and a Hagedorn transition of the thermal ensemble. The strong coupling duals of the Galilean superstring theories are considered and are shown to be described by an eleven-dimensional Galilean invariant theory of light membrane fluctuations. A new class of Galilean invariant nongravitational theories of light-brane excitations are obtained. We exhibit dual formulations of the strong coupling limits of these Galilean invariant theories and show that they exhibit many of the conventional dualities of M theory in a nonrelativistic setting. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We study the D-brane spectrum of 풩 = 2 string orbifold theories using the boundary state formalism. The construction is carried out for orbifolds with isolated singularities, non-isolated singularities and orbifolds with discrete torsion. Our results agree with the corresponding K-theoretic predictions when they are available and generalize them when they are not. This suggests that the classification of boundary states provides a sort of ``quantum K-theory'' just as chiral rings in CFT provide ``quantum'' generalizations of cohomology. We discuss the identification of these states with D-branes wrapping holomorphic cycles in the large radius limit of the CFT moduli space. The example ℂ3/ℤ3 is worked out in full detail using local mirror symmetry techniques. We find a precise correspondence between fractional branes at the orbifold point and configurations of D-branes described by vector bundles on the exceptional ℙ2 cycle. [ABSTRACT FROM AUTHOR]