Nonrelativistic near-BPS corners of $$ \mathcal{N} $$ = 4 super-Yang-Mills with SU(1, 1) symmetry

We consider limits of $$ \mathcal{N} $$ N = 4 super Yang-Mills (SYM) theory that approach BPS bounds and for which an SU(1,1) structure is preserved. The resulting near-BPS theories become non-relativistic, with a U(1) symmetry emerging in the limit that implies the conservation of particle number. They are obtained by reducing $$ \mathcal{N} $$ N = 4 SYM on a three-sphere and subsequently integrating out fields that become non-dynamical as the bounds are approached. Upon quantization, and taking into account normal-ordering, they are consistent with taking the appropriate limits of the dilatation operator directly, thereby corresponding to Spin Matrix theories, found previously in the literature. In the particular case of the SU(1,1—1) near-BPS/Spin Matrix theory, we find a superfield formulation that applies to the full interacting theory. Moreover, for all the theories we find tantalizingly simple semi-local formulations as theories living on a circle. Finally, we find positive-definite expressions for the interactions in the classical limit for all the theories, which can be used to explore their strong coupling limits. This paper will have a companion paper in which we explore BPS bounds for which a SU(2,1) structure is preserved.

Interpreting plural predication: homogeneity and non-maximality

Plural definite descriptions across many languages display two well-known properties. First, they can give rise to so-called non-maximal readings, in the sense that they ‘allow for exceptions’ (Mary read the books on the reading list, in some contexts, can be judged true even if Mary didn’t read all the books on the reading list). Second, while they tend to have a quasi-universal quantificational force in affirmative sentences (‘quasi-universal’ rather than simply ‘universal’ due to the possibility of exceptions we have just mentioned), they tend to be interpreted existentially in the scope of negation (a property often referred to as homogeneity, cf. Löbner in Linguist Philos 23:213–308, 2000). Building on previous works (in particular Krifka in Proceedings of SALT VI, Cornell University, pp 136–153, 1996 and Malamud in Semant Pragmat, 5:1–28, 2012), we offer a theory in which sentences containing plural definite expressions trigger a family of possible interpretations, and where general principles of language use account for their interpretation in various contexts and syntactic environments. Our theory solves a number of problems that these previous works encounter, and has broader empirical coverage in that it offers a precise analysis for sentences that display complex interactions between plural definites, quantifiers and bound variables, as well as for cases involving non-distributive predicates. The resulting proposal is briefly compared with an alternative proposal by Križ (Aspects of homogeneity in the semantics of natural language, University of Vienna, 2015), which has similar coverage but is based on a very different architecture and sometimes makes subtly different predictions.

Definite expression and degrees of definiteness

This chapter studies definite determiners formerly treated as semantic expletives and challenges the view that they can be uniformly treated as such. Assuming that definiteness consists of two features, uniqueness (iota) and familiarity (Fam), and depending on the features spelled out by the determiner, it proposes that definite articles can be fully specified for definiteness spelling out both features (full definiteness), partially specified, spelling out Fam (partial definiteness), or, in the case of true expletives, not specified at all (zero definiteness). Fully definite expressions cannot be modified by other definite nominals. In contrast, partially definite expressions form predicative FamPs, which can be modified by other definite nominals. Fam can also introduce proper names and generic kind-denoting nouns. Finally, true expletives appear even in non-definite contexts. An explanatory and descriptive account is offered that provides new insights on the properties of definiteness.

On the (in)definiteness of impersonal pronouns

This paper addresses the question whether impersonal pronouns should be analyzed as indefinite or definite expressions based on their discourse anaphoric potential. I present new data that support the claim that impersonal pronouns should be analyzed as neither (see Koenig & Mauner 1999). I sketch a formal analysis that captures this behaviour. Furthermore, I show that the availability of quantificational variability effects for impersonal pronouns is not foolproof evidence for their indefiniteness as is usually assumed in the literature (see Malamud 2013).

Restrictions on definiteness in the grammars of German-Turkish heritage speakers

This paper reports on a study investigating restrictions on definiteness (the Definiteness Effect) in existential constructions in the two languages of Turkish heritage speakers in Germany. Turkish and German differ in how the Definiteness Effect plays out. Definite expressions in German may not occur in affirmative or negative existentials, whereas in Turkish the restriction applies only to affirmative existentials. Participants were adults and fell into two groups: simultaneous bilinguals (2L1) who acquired German before age 3 and early sequential bilinguals (2L1) who acquired German after age 4; there were also monolingual controls. The tasks involved acceptability judgments. Subjects were presented with contexts, each followed by a sentence to be judged, including grammatical and ungrammatical existentials. Results show that the bilinguals, regardless of age of acquisition, make judgments appropriate for each language. They reject definite expressions in negative existentials in German and accept them in Turkish, suggesting distinct grammars.

Possessive phrases as definite expressions in Tupí-Guaraní languages: the role of the R-morphology

O estudo investiga a sintaxe de sintagmas possessivos em línguas da família Tupí-Guaraní, considerando em particular a hipótese de que a chamada morfologia-R(elacional) denota uma descrição definida, induzindo efeito de definitude. Assumindo a Hipótese-DP, argumenta-se que a morfologia-R no nome que denota o possuidor codifica lexicalmente o núcleo D, por meio de uma relação de agreement, que licencia o possuidor, e permite incluir as línguas TG no grupo de línguas do tipo D(eterminante) G(enitivo), em oposição às línguas do tipo A(djetivo) G(enitivo).

The semantics of definite expressions and the grammaticalization of THE

This paper explores the claim that definite expressions involve universal and existential quantification from the point of view of Word Grammar, in order to establish whether the quantificational view of definiteness is compatible with a particular cognitive theory of language, and to see how it compares with the familiarity treatment of definiteness. It is argued that the quantificational approach is superior to the familiarity approach in the analysis of a number of linguistic phenomena, and a number of Word Grammar analyses are presented. The paper concludes with an investigation into the grammaticalization of the English definite article, in order to compare the merits of the two approaches, and argues that the quantificational approach delivers a simpler and preferable account.

Restrictions on definiteness in second language acquisition

In this paper we investigate whether learners of L2 English show knowledge of the Definiteness Effect (Milsark, 1977), which restricts definite expressions from appearing in the existential there-insertion construction. There are crosslinguistic differences in how restrictions on definiteness play out. In English, definite expressions may not occur in either affirmative or negative existentials (e.g. There is a/*the mouse in my soup; There isn’t a/*the mouse in my soup). In Turkish and Russian, affirmative existentials observe a restriction similar to English, whereas negative existentials do not. We report on a series of experiments conducted with learners of English whose L1s are Turkish and Russian, of intermediate and advanced proficiency. Native speakers also took the test in English, Turkish, and Russian. The task involved acceptability judgments. Subjects were presented with short contexts, each followed by a sentence to be judged as natural/unnatural. Test items included affirmative and negative existentials, as well as items testing apparent exceptions to definiteness restrictions. Results show that both intermediate and advanced L2ers respond like English native speakers, crucially rejecting definites in negative existentials. A comparison with the groups taking the test in Russian and Turkish confirms that judgments in the L2 are quite different from the L1, suggesting that transfer cannot provide the explanation for learner success.