Yaron Oz

Gluon scattering in deformed N=4 SYM

We consider gluon and gluino scattering amplitudes in large Nβ -deformed N = 4 SYM with real β. A direct inspection of the planar diagrams shows that the scattering amplitudes to all orders in perturbation theory are the same as in the undeformed N = 4 SYM theory. Using the dual σ -model description, we find the same equality at strong coupling to all orders in the σ -model loop expansion. Finally, we show that the same analysis holds for gluon scattering amplitudes in a three-parameter deformation of planar N = 4 SYM that breaks all the supersymmetry.

Anomaly cancellation in extended phase space. The chiral Schwinger model

Abstract Quantum mechanically broken symmetries can be restored by properly extending the initial phase space to include extra degrees of freedom. The chiral Schwinger model is an ideal example in which general methods for restoration of a quantum mechanically broken symmetry can be studied. Here we construct an extended phase space, following recent ideas of Batalin and Fradkin in which quantum mechanically induced second-class constraints in the original system are made first class in the corresponding symmetric system. In the extended phase space, the anomalous theory can be viewed as a gauge fixed (a “unitary gauge”) version of the new symmetric theory. Once this corresponding symmetric theory is determined, one can exploit the restored gauge symmetry and the freedom of fixing the gauge. Different gauges can be employed which reflect different physical aspects of the theory in a more transparent way than in the original gauge fixed (anomalous) theory. The particular restoration of symmetry used here is compared to the more conventional approach of adding a Wess-Zumino term to the action or adding extra right-handed fermions.

Chiral matter coupled to two-dimensional quantum gravity

Chiral matter coupling to two-dimensional quantum gravity is analyzed in the light-cone gauge. This theory exhibits both conformal and gravitational anomalies. The anomalous Ward identities are integrated and yield recursion relations among the correlation functions. An underlying SL(2, ℝ) × U(1) current algebra is revealed. Exact formula for the SL(2, ℝ) central charge and a relation connecting scaling dimensions and spin of fields are derived. The exact results and the renormalization of the U(1) charge of the fermion field are checked to one-loop order.

BFV-BRST quantization of anomalous d=2 non-abelian chiral theory☆

Abstract Working in the hamiltonian formalism, we show that the anomalous theory of N Dirac fermions, chirally coupled to a U (N) gauge field in two dimensions, is a gauge fixed symmetric theory. Thus, one may work with the gauge symmetric theory instead of its gauge fixed version — the anomalous one. Using the BFV-BRST procedure we quantize the symmetric theory, and show that the theory is formally consistent and unitary provided a > 1, where a denotes an arbitrary regularization parameter appearing in the quantum theory. We comment on the advantage of working with the symmetric theory for the investigation of the renormalization properties of the anomalous theory.

The spectrum of the 2D Black Hole, or Does the 2D black hole have tachyonic or W--hair?

We solve the equations of motion of the tachyon and the discrete states in the background of Wittens semiclassical black hole and in the exact 2D dilaton-graviton background of Dijkgraaf et al. We find the exact solutions for weak fields, leading to conclusions in disagreement with previous studies of tachyons in the black hole. Demanding that a state in the black hole be well behaved at the horizon implies that it must tend asymptotically to a combination of a Seiberg and an anti-Seiberg c=1 state. For such a state to be well behaved asymptotically, it must satisfy the condition that neither its Seiberg nor its anti-Seiberg Liouville momentum is positive. Thus, although the free-field BRST cohomologies of the underlying SL(2,R)/U(1) theory is the same as that of a c=1 theory, the black hole spectrum is drastically truncated: THERE ARE NO W_INFINITY STATES, AND ONLY TACHYONS WITH X-MOMENTA | P_TACH | <= | M_TACH | ARE ALLOWED. In the Minkowski case only the static tachyon is allowed. The black hole is stable to the back reaction of these remaining tachyons, so they are good perturbations of the black hole, or ``hair. However, this leaves only 3 tachyonic hairs in the black hole and 7 in the exact solution! Such sparse hair is clearly irrelevant to the maintenance of coherence during black hole evaporation.

Renormalization structure of non-abelian chiral bosons coupled to a gauge field

Abstract We write the non-covariant action, describing non-abelian chiral bosons coupled to a gauge field, in a “curved” space-time covariant form, and study its renormalization structure. Exploiting the observation that the theory may be considered as a gauge fixed version of a gauge invariant theory, and working in a covariant gauge, we show that the theory is one-loop renormalizable and compute the one-loop β-function. Due to a property of the “curved” metric, the renormalization structure of the theory is similar to that of Dirac fermions chirally coupled to a non-abelian gauge field.

Two-dimensional chirally induced quantum gravity

Abstract Two-dimensional quantum gravity induced by chiral matter is analyzed in the light-cone gauge. This theory exhibits both conformal and gravitational anomalies. The anomalies Ward identities are integrated and yield recursion relations among the correlation functions. An underlying SL(2, R )×U(1) current algebra i s revealed.

Renormalization properties of anomalous d = 2 non-Abelian chiral theory☆

Abstract Exploiting the fact that the anomalous theory of N Dirac fermions, chirally coupled to a U ( N ) gauge field in two dimensions, is a gauge fixed symmetric theory, we study its renormalization properties. Working in a covariant gauge, we compute the one-loop renormalization counterterm and show, that a — an arbitrary parameter appearing in the theory and determining its unitarity – is renormalized unless it is equal to zero or two. These two values, which are zeros of the one-loop β-function, correspond, probably, to fixed points of the theory. We conjecture that this anomalous theory is perturbatively renormalizable to all orders.

Non-abelian chiral bosons coupled to gauge field

Abstract By imposing constraints on the phase space of the bosonic description of N Dirac fermions, chirally coupled to a U( N ) gauge field in two dimensions, we construct a natural coupling of non-abelian chiral bosons to a gauge field. Analysing the constraints structure of the theory we show that non-abelian chiral bosons coupled to a gauge field may be viewed as a gauge fixed version of a gauge invariant theory. Using the hamiltonian BRST formalism we quantize the theory and derive a unitarity restriction.

Bosonized actions for anomalous gauge theories on coadjoint orbits

Abstract Starting from the extended Lie algebras generated by the Gauss-law constraints, and using the coadjoint-orbit method, we construct bosonized actions for anomalous gauge theories in two and four space-time dimensions. We show that the anomalous gauge algebras determine the anomalous part of the actions, but not the gauge invariant terms. These are generated by exact cocycles.