34 research outputs found
N=(0, 2) Deformation of (2, 2) Sigma Models: Geometric Structure, Holomorphic Anomaly and Exact Beta Functions
We study N=(0,2) deformed (2,2) two-dimensional sigma models. Such heterotic
models were discovered previously on the world sheet of non-Abelian strings
supported by certain four-dimensional N=1 theories. We study geometric aspects
and holomorphic properties of these models, and derive a number of exact
expressions for the beta functions in terms of the anomalous dimensions
analogous to the NSVZ beta function in four-dimensional Yang-Mills. Instanton
calculus provides a straightforward method for the derivation. The anomalous
dimensions are calculated up to two loops implying that one of the beta
functions is explicitly known up to three loops. The fixed point in the ratio
of the couplings found previously at one loop is not shifted at two loops. We
also consider the N=(0,2) supercurrent supermultiplet (the so-called
hypercurrent) and its anomalies, as well as the "Konishi anomaly." This gives
us another method for finding exact functions. We prove that despite
the chiral nature of the models under consideration quantum loops preserve
isometries of the target space.Comment: 38 pages, 6 figures, minor changes in the text and references, the
journal versio
Spectral Flow in Instanton Computations and the \boldmath{\b} functions
We discuss various differences in the instanton-based calculations of the
functions in theories such as Yang-Mills and on
one hand, and theory with Symanzik's sign-reversed prescription
for the coupling constant on the other hand. Although the
aforementioned theories are asymptotically free, in the first two theories,
instantons are topological, whereas the Fubini-Lipatov instanton in the third
theory is topologically trivial. The spectral structure in the background of
the Fubini-Lipatov instanton can be continuously deformed into that in the flat
background, establishing a one-to-one correspondence between the two spectra.
However, when considering topologically nontrivial backgrounds for Yang-Mills
and theories, the spectrum undergoes restructuring. In
these cases, a mismatch between the spectra around the instanton and the
trivial vacuum occurs.Comment: 22 page
Four-fermion deformations of the massless Schwinger model and confinement
We consider the massless charge- Schwinger model and its deformation with
two four-fermion operators. Without the deformations, this model exhibits
chiral symmetry breaking without confinement. It is usually asserted that the
massless Schwinger model is always deconfined and a string tension emerges only
when a mass for the fermion field is turned on. We show that in the presence of
these four-fermion operators, the massless theory can in fact confine. One of
the four-fermion deformations is chirally neutral, and is a marginal
deformation. The other operator can be relevant or irrelevant, and respects a
subgroup of chiral symmetry for even , hence forbidding a
mass term. When it is relevant, even the exactly massless theory exhibits both
confinement and spontaneous chiral symmetry breaking. The construction is
analogous to QCD(adj) in 2d. While the theory without four-fermion deformations
is deconfined, the theory with these deformations is generically in a confining
phase. We study the model on using bosonization, and also
analyze the mechanism of confinement on , where we find
that confinement is driven by fractional instantons.Comment: 38 pages, 5 figures; v2: minor improvement
Enhanced Worldvolume Supersymmetry and Intersecting Domain Walls in N=1 SQCD
We study the worldvolume dynamics of BPS domain walls in N=1 SQCD with N_f=N
flavors, and exhibit an enhancement of supersymmetry for the reduced moduli
space associated with broken flavor symmetries. We provide an explicit
construction of the worldvolume superalgebra which corresponds to an N=2 Kahler
sigma model in 2+1D deformed by a potential, given by the norm squared of a
U(1) Killing vector, resulting from the flavor symmetries broken by unequal
quark masses. This framework leads to a worldvolume description of novel
two-wall junction configurations, which are 1/4-BPS objects, but nonetheless
preserve two supercharges when viewed as kinks on the wall worldvolume.Comment: 35 pages, 3 figures; v2: minor corrections and a reference added, to
appear in Phys. Rev.
Counting Domain Walls in N=1 Super Yang-Mills Theory
We study the multiplicity of BPS domain walls in N=1 super Yang-Mills theory,
by passing to a weakly coupled Higgs phase through the addition of fundamental
matter. The number of domain walls connecting two specified vacuum states is
then determined via the Witten index of the induced worldvolume theory, which
is invariant under the deformation to the Higgs phase. The worldvolume theory
is a sigma model with a Grassmanian target space which arises as the coset
associated with the global symmetries broken by the wall solution. Imposing a
suitable infrared regulator, the result is found to agree with recent work of
Acharya and Vafa in which the walls were realized as wrapped D4-branes in IIA
string theory.Comment: 28 pages, RevTeX, 3 figures; v2: discussion of the index slightly
expanded, using an alternative regulator, and references added; v3: typos
corrected, to appear in Phys. Rev.