Nonhermitian Supersymmetric Partition Functions: the case of one bosonic flavor

Non-Fermi liquid behavior of large N_B quantum critical metals

The problem of continuous quantum phase transitions in metals involves critical bosons coupled to a Fermi surface. We solve the theory in the limit of a large number, N_B, of bosonic flavors, where the bosons transform in the adjoint representation, while the fermions are in the fundamental representation of a global SU(N_B) flavor symmetry group. The leading large N_B solution corresponds to a non-Fermi liquid coupled to Wilson-Fisher bosons. In a certain energy range, the fermion velocity vanishes - resulting in the destruction of the Fermi surface. Subleading 1/N_B corrections correspond to…

QED's in $2{+}1$ dimensions: complex fixed points and dualities

We consider Quantum Electrodynamics with an even number $N_f$ of bosonic or fermionic flavors, allowing for interactions respecting at least $U(N_f/2)^2$ global symmetry. Both in the bosonic and in the fermionic case, we find four interacting fixed points: two with $U(N_f/2)^2$ symmetry, two with $U(N_f)$ symmetry. Large $N_f$ arguments suggest that, lowering $N_f$, all these fixed points merge pairwise and become complex CFT's. In the bosonic QED's the merging happens around $N_f\sim 9{-}11$ and does not break the global symmetry. In the fermionic QED's the merging happens around $N_f\sim3{-}…

SUSY Relics in One-Flavor QCD from a New 1/N Expansion

We suggest a new large-N_c limit for multi flavor QCD. Since fundamental and two-index antisymmetric representations are equivalent in SU(3), we have the option to define SU(N_c) QCD keeping quarks in the latter. We can then define a new 1/N_c expansion (at fixed number of flavors N_f) that shares appealing properties with the topological (fixed N_f/N_c) expansion while being more suitable for theoretical analysis. In particular, for N_f=1, our large-N_c limit gives a theory that we recently proved to be equivalent, in the bosonic sector, to N=1 supersymmetric gluodynamics. Using known propert…

Unquenched QCD Dirac Operator Spectra at Nonzero Baryon Chemical Potential

The microscopic spectral density of the QCD Dirac operator at nonzero baryon chemical potential for an arbitrary number of quark flavors was derived recently from a random matrix model with the global symmetries of QCD. In this paper we show that these results and extensions thereof can be obtained from the replica limit of a Toda lattice equation. This naturally leads to a factorized form into bosonic and fermionic QCD-like partition functions. In the microscopic limit these partition functions are given by the static limit of a chiral Lagrangian that follows from the symmetry breaking patter…

Non-Abelian Chern-Simons Vortices

We consider the bosonic sector of a N=2 supersymmetric Chern-Simons-Higgs theory in 2+1 dimensions. The gauge group is U(1)xU(N) and has N_f flavors of fundamental matter fields. The model supports non-Abelian (axially symmetric) vortices when N_f\geq N, which have internal (orientational) moduli. When N_f > N, the solutions acquire additional collective coordinates parameterizing their transverse size. We solve the BPS equations numerically and obtain local (N_f = N) and semi-local (N_f > N) string solutions.

Holographic nonlinear hydrodynamics from AdS/CFT with multiple/non-Abelian symmetries

We study viscous hydrodynamics of hot conformal field theory plasma with multiple/non-Abelian symmetries in the framework of AdS/CFT correspondence, using a recently proposed method of directly solving bulk gravity in derivative expansion of local plasma parameters. Our motivation is to better describe the real QCD plasma produced at RHIC, incorporating its U(1)^Nf flavor symmetry as well as SU(2)_I non-Abelian iso-spin symmetry. As concrete examples, we choose to study the STU model for multiple U(1)^3 symmetries, which is a sub-sector of 5D N=4 gauged SUGRA dual to N=4 Super Yang-Mills theor…

Predictions for QCD from Supersymmetry

We review the construction of the effective Lagrangians of the Veneziano-Yankielowicz (VY) type for two non-supersymmetric theories containing one Dirac fermion in the two-index antisymmetric or symmetric representation of the gauge group (orientifold theories). Since these theories are planar equivalent, at N\to\infty to super Yang-Mill their effective Lagrangians coincides with the bosonic part of the VY Lagrangian. We depart from the supersymmetric limit in two ways. First, we consider finite but still large values of N. Then 1/N effects break supersymmetry. We suggest a minimal modificatio…

Composite Inflation from Super Yang-Mills, Orientifold and One-Flavor QCD

Recent investigations have shown that inflation can be driven by four-dimensional strongly interacting theories non-minimally coupled to gravity. We explore this paradigm further by considering composite inflation driven by orientifold field theories. The advantage of using these theories resides in the fact that at large number of colors they feature certain super Yang-Mills properties. In particular we can use for inflation the bosonic part of the Veneziano-Yankielowicz effective theory. Furthermore, we include the 1/N as well as fermion mass corrections at the effective Lagrangian level all…

单味量子色动力学的谱：超对称动力学的一扇窗口

Spectrum of QCD with one flavor: A window for supersymmetric dynamics

本研究计算单味量子色动力学中低能介子谱，采用改进威尔逊费米子方法处理费米子行列式负值问题，对比大N极限下有效场论预测，为超对称动力学研究提供新窗口。

Infrared phases of 3d massless CS-QCD and large $N_f$

We compute anomalous dimensions of quartic operators which are singlets under the $\mathrm{U}(N_f)$ global symmetry in Yang-Mills theories with Chern-Simons level $k$ in three dimensions coupled to $N_f$ Dirac fermions. In order to have analytic control, we consider the regime $N_f\gg N_c\gg 1$, where the problem is reduced to the study of a flavor-adjoint and a flavor-singlet bilinears whose square give the quartic operators of interest. We provide evidence that these operators hit marginality, signaling instabilities which, for $\frac{2k}{N_f}<1$ suggest the spontaneous breaking of the globa…

Effective Lagrangians for Orientifold Theories

We construct effective Lagrangians of the Veneziano-Yankielowicz (VY) type for two non-supersymmetric theories which are orientifold daughters of supersymmetric gluodynamics (containing one Dirac fermion in the two-index antisymmetric or symmetric representation of the gauge group). Since the parent and daughter theories are planar equivalent, at N\to\infty the effective Lagrangians in the orientifold theories basically coincide with the bosonic part of the VY Lagrangian. We depart from the supersymmetric limit in two ways. First, we consider finite (albeit large) values of N. Then 1/N effects…

Pseudo-Goldstone excitations in chiral Yukawa-theories with quadratic explicit symmetry breaking

The symmetry breakdown pattern is studied in models containing one fermion flavor multiplet and a multicomponent scalar field, supplemented with a chiral Yukawa-interaction, and in presence of an explicit symmetry breaking source quadratic in the scalar field. In a detailed investigation of the model with $U_L(1) \times U_R(1)$ chiral symmetry it is shown that by diminishing the strength of quadratic explicit symmetry breaking one can still keep stable the mass ratio of the fermionic and the pseudo-Goldstone excitation. At the same time the mass ratio of the two bosonic excitations appears to …