A roadmap for bootstrapping critical gauge theories: decoupling operators of conformal field theories in $d>2$ dimensions

We propose a roadmap for bootstrapping conformal field theories (CFTs) described by gauge theories in dimensions d>2d>2. In particular, we provide a simple and workable answer to the question of how to detect the gauge group in the bootstrap calculation. Our recipe is based on the notion of decoupling operator, which has a simple (gauge) group theoretical origin, and is reminiscent of the null operator of 2d2d Wess-Zumino-Witten CFTs in higher dimensions. Using the decoupling operator we can efficiently detect the rank (i.e. color number) of gauge groups, e.g., by imposing gap conditions in the CFT spectrum. We also discuss the physics of the equation of motion, which has interesting consequences in the CFT spectrum as well. As an application of our recipes, we study a prototypical critical gauge theory, namely the scalar QED which has a U(1)U(1) gauge field interacting with critical bosons. We show that the scalar QED can be solved by conformal bootstrap, namely we have obtained its kinks and islands in both d=3d=3 and d=2+\epsilond=2+ϵ dimensions.

ON CAUCHY-RIEMANN STRUCTURES AND THE GENERAL EVEN ORDER STRUCTURE

The present paper aims to study the Cauchy-Riemann structures and the general even order structure and find the general even order structure that acts on complementary distributions and as an almost complex structure and a null operator, respectively. We also discuss integrability conditions and prove certain theorems on the Cauchy-Riemann structures and the general even order structure. Moreover, we construct examples of it.

Relative nominals and event nominals in Hiaki

In ‘Relative nominals and event nominals in Hiaki’, Harley discusses an interesting formal overlap between nominalizations which create relative-clause like structures and nominalizations which create event nominals in Hiaki (Yaqui). The nominalizer which usually derives a subject relative nominal, when applied to an argumentless predicate such as a weather verb or an impersonal passive, also derives an event nominal. Harley argues that this is because the event argument IS the ‘subject’ of an argumentless predicate, the only accessible argument for the nominalizer to reify. In the process of proposing a uniform semantics for the relative nominalizers and the event nominalizer, a detailed analysis of both is provided. The nominalizers are argued to select an AspP complement. In entity-referring relative nominals, null operator movement is involved; in the event-referring event nominals, no operator is needed or possible. The syntax and morphology of the relative nominalizers is worked out in detail, with particular attention to the genitive-marked subjects of object, oblique, and locative relative nominals. <163>

The Middle Construction in Minimalist Syntax: English and Slovenian

The paper discusses the argument structure of the English middle construction and its Slovenian equivalent from the perspective of minimalist syntax. The paper first introduces Bruening’s (2012) recent approach to syntactic middle formation, which posits that middle sentences are derived via an operator that existentially quantifies over the open agent variable introduced by an active Voice projection. Subsequently, the paper argues that the adverbial modifier in the middle construction is not a semantic argument of the null operator, contra Bruening (2012). Finally, the paper proposes that the reflexive morpheme se in the related Slovenian se-sentences plays a role of valency reduction similar to that of the null English operator.

Intervention in tough-constructions revisited

In this paper, we subject to closer scrutiny one particularly influential recent argument in favour of the long-movement analysis of tough-constructions. Hartman (2011, 2012a, 2012b) discovered that experiencer PPs lead to ungrammaticality in tough-constructions, but not in expletive constructions. He attributes this ungrammaticality to defective intervention of A-movement, a movement step crucially postulated only in the long-movement analysis. He takes this as evidence that tough-constructions are derived via long movement. We make the novel observation that a PP intervention effect analogous to that in tough-constructions also arises in constructions that do not involve A-movement, namely pretty-predicate constructions and gapped degree phrases. Consequently, the intervention effect does not provide an argument for an A-movement step in tough-constructions or for the long-movement analysis, but rather for the base-generation analysis. We develop a uniform account of the intervention effects as a semantic-type mismatch. In particular, we propose that what unifies tough-constructions, pretty-predicate constructions, and gapped degree phrases is that they all have an embedded clause that is a null-operator structure. Introducing an experiencer PP into these constructions creates an irresolvable semantic-type mismatch. As such, we argue for a reassessment of what appears to be a syntactic locality constraint as an incompatibility in the semantic composition.

A Case of V2 in Chinese

As far as the left periphery is concerned, there is a conspiracy between syntax, semantics, and pragmatics to ensure the success of sentence formation. We would like to put forth the claim that peripheral features play an important role in this endeavor, which can be checked by either Merge or Move according to the parameter-settings of individual languages. Along this line, topic prominence can be regarded as the result of peripheral feature checking, and the null topic hypothesis à la Huang (1984) is reinvented as a null operator merger to fulfill interface economy in the left periphery. In this regard, Chinese provides substantial evidence from obligatory topicalization in outer affectives, evaluatives, and refutory wh-constructions, which applies only when the licensing from a D(efiniteness)-operator is blocked. The idea also extends naturally to the issues concerning pro-drop and bare nominals in general. In this light, we may well compare Chinese obligatory topicalization to those residual cases of verb-second (V2) in English, all being manifestation of the strong uniformity.

How relative are purpose relative clauses?

In this paper, we present extended argumentation against a raising analysis for every type of relative clauses. Specifically, we argue that purpose relative clauses involve raising of a null operator to Spec,CP, contrary toAfter showing that all purpose relatives in European Portuguese are CPs, we present several arguments in favor of a null operator analysis of this type of structure. First, we show that parasitic gap effects support the existence of a variable in object purpose relatives and in VP adjunct purpose clauses with an object gap. We then show that Principle A effects in object purpose relatives allow to distinguish this type of relatives from