We discuss the BRST quantization of General Relativity (GR) with a cosmological constant in the unimodular gauge. We show how to gauge fix the transverse part of the diffeomorphism and then further to fulfill the unimodular gauge. This process requir
es the introduction of an additional pair of BRST doublets which decouple from the physical sector together with the other three pairs of BRST doublets for the transverse diffeomorphism. We show that the physical spectrum is the same as GR in the usual covariant gauge fixing. We then suggest to define the quantum theory of Unimodular Gravity (UG) by making Fourier transform of GR in the unimodular gauge with respect to the cosmological constant and slightly generalizing it. This suggests that the quantum theory of UG may describe the same theory as GR but the spacetime volume is fixed. We also discuss problems left in this formulation of UG.
In general coordinate invariant gravity theories whose Lagrangians contain arbitrarily high order derivative fields, the Noether currents for the global translation and for the Nakanishis IOSp(8|8) choral symmetry containing the BRS symmetry as its m
ember, are constructed. We generally show that for each of those Noether currents a suitable linear combination of equations of motion can be brought into the form of Maxwell-type field equation possessing the Noether current as its source term.
A scenario based on the scale invariance for explaining the vanishing cosmological constant (CC) is discussed. I begin with a notice on the miraculous fact of the CC problem that the vacuum energies totally vanish at each step of hierarchical and suc
cessive spontaneous symmetry breakings. I then argue that the classical scale invariance is a necessary condition for the calculability of the vacuum energy. Next, I discuss how sufficient the scale invariance is for solving the CC problem. First in the framework of classical field theory, the scale invariance is shown to give a natural mechanism for realizing the miracle of vanishing vacuum energies at every step of spontaneous symmetry breakings. Then adopting Englert-Truffin-Gastmans prescription to maintain the scale invariance in quantum field theory, I point out that the quantum scale invariance alone is not yet sufficient to avoid the superfine tuning of coupling constants for realizing vanishingly small cosmological constant, whereas the hierarchy problem may be solved. Another symmetry or a mechanism is still necessary which protects the flat direction of the potential against the radiative corrections.
It is recently shown that in 4D $SU(N)$ Nambu--Jona-Lasinio (NJL) type models, the $SU(N)$ symmetry breaking into its special subgroups is not special but much more common than that into the regular subgroups, where the fermions belong to complex rep
resentations of $SU(N)$. We perform the same analysis for $SO(N)$ NJL model for various $N$ with fermions belonging to an irreducible spinor representation of $SO(N)$. We find that the symmetry breaking into special or regular subgroups has some correlation with the type of fermion representations; i.e., complex, real, pseudo-real representations.
The purpose of this paper is to show that the symmetry breaking into special subgroups is not special at all, contrary to the usual wisdom. To demonstrate this explicitly, we examine dynamical symmetry breaking pattern in 4D $SU(N)$ Nambu--Jona-Lasin
io type models in which the fermion matter belongs to an irreducible representation of $SU(N)$. The potential analysis shows that for almost all cases at the potential minimum the $SU(N)$ group symmetry is broken to its special subgroups such as $SO(N)$ or $USp(N)$ when symmetry breaking occurs.
The supersymmetric Nambu-Jona-Lasinio model proposed by Cheng, Dai, Faisel and Kong is re-analyzed by using an auxiliary superfield method in which a hidden local U(1) symmetry emerges. It is shown that, in the healthy field-space region where no neg
ative metric particles appear, only SUSY preserving vacua can be realized in the weak coupling regime and a composite massive spin-1 supermultiplets appear as a result of spontaneous breaking of the hidden local U(1) symmetry. In the strong coupling regime, on the other hand, SUSY is dynamically broken, but it is always accompanied by negative metric particles.
In $D=4$, $cal{N}=1$ conformal superspace, the Yang-Mills matter coupled supergravity system is constructed where the Yang-Mills gauge interaction is introduced by extending the superconformal group to include the Kahler isometry group of chiral matt
er fields. There are two gauge-fixing procedures to get to the component Poincare supergravity: one via the superconformal component formalism and the other via the Poincare superspace formalism. These two types of superconformal gauge-fixing conditions are analyzed in detail and their correspondence is clarified.
The superspace formulation of N=1 conformal supergravity in four dimensions is demonstrated to be equivalent to the conventional component field approach based on the superconformal tensor calculus. The detailed correspondence between two approaches
is explicitly given for various quantities; superconformal gauge fields, curvatures and curvature constraints, general conformal multiplets and their transformation laws, and so on. In particular, we carefully analyze the curvature constraints leading to the superconformal algebra and also the superconformal gauge fixing leading to Poincare supergravity since they look rather different between two approaches.
We discuss the no-ghost theorem in the massive gravity in a covariant manner. Using the BRST formalism and St{u}ckelberg fields, we first clarify how the Boulware-Deser ghost decouples in the massive gravity theory with Fierz-Pauli mass term. Here we
find that the crucial point in the proof is that there is no higher (time) derivative for the St{u}ckelberg `scalar field. We then analyze the nonlinear massive gravity proposed by de Rham, Gabadadze and Tolley, and show that there is no ghost for general admissible backgrounds. In this process, we find a very nontrivial decoupling limit for general backgrounds. We end the paper by demonstrating the general results explicitly in a nontrivial example where there apparently appear higher time derivatives for St{u}ckelberg scalar field, but show that this does not introduce the ghost into the theory.
The gauge-fixing problem of modified cubic open superstring field theory is discussed in detail both for the Ramond and Neveu-Schwarz sectors in the Batalin-Vilkovisky (BV) framework. We prove for the first time that the same form of action as the cl
assical gauge-invariant one with the ghost-number constraint on the string field relaxed gives the master action satisfying the BV master equation. This is achieved by identifying independent component fields based on the analysis of the kernel structure of the inverse picture changing operator. The explicit gauge-fixing conditions for the component fields are discussed. In a kind of $b_0=0$ gauge, we explicitly obtain the NS propagator which has poles at the zeros of the Virasoro operator $L_0$.
