Dimensionality aspects of non-minimal electromagnetic couplings are investigated. By means of the Foldy-Wouthuysen transformation, we attain (non-)relativistic interactions related to the non-minimal coupling in three-dimensional spacetime, for both the bosonic and fermionic fields. Next, we establish some comparisons and analyse particular situations in which the external electromagnetic fields are described either by Maxwell or Maxwell-Chern-Simons Electrodynamics. In addition, we consider the situation of a non-minimal coupling for the fermionic field in four dimensions, carry out its dimensional reduction to three dimensions and show that the three-dimensional scenario previously worked out can be recovered as a particular case. Finally, we discuss a number of structural aspects of both procedures.
We construct noncommutative versions of both the minimal and the new minimal supersymmetric Grand Unified Theories. The enveloping-algebra formalism is used to carry out such constructions. The beautiful formulation of the Higgs sector of these noncommutative theories is a consequence of fact that, in the GUTs at hand, the ordinary Higgs fields can be realized as elements of the Clifford algebra Cl10(C). In the noncommutative supersymmetric GUTs we formulate, supersymmetry is linearly realized by the noncommutative fields; but it is not realized by the ordinary fields that define those noncomm…
We study Kramers-Wannier dualities for Wess-Zumino-Witten theories and (super-)minimal models in the Cardy case, i.e. the case with bulk partition function given by charge conjugation. Using the TFT approach to full rational conformal field theories, we classify those dualities that preserve all chiral symmetries. Dualities turn out to exist for small levels only.
The aim of this note is to address the low energy limit of quantum field theories with a minimal length scale. The essential feature of these models is that the minimal length acts as a regulator in the asymptotic high energy limit which is incorporated through an infinite series of higher order derivatives. If one investigates a perturbative expansion in inverse powers of the Planck mass, one generically obtains extra poles in the propagator, and instabilities connected with the higher order derivative Lagrangian, that are however artifacts of truncating the series.
We consider a real scalar field and a Majorana fermion field to construct a supersymmetric quantum theory of free fermion fields based on the deformed Heisenberg algebra $[x,p]=i\hbar\big(1-βp+2β^{2}p^{2}\big)$, where $β$ is a deformation parameter. We present a deformed supersymmetric algebra in the presence of minimal length and maximal momentum.
We perform a first step analysis toward generalization of the classification of N=4 linear quiver gauge theories by Gaiotto and Witten including Chern-Simons interaction. For this we investigate minimal N=4 U(N_1)_k x U(N_2)_{-k} Chern-Simons theories and their superconformal indices. In the previous publication we analyzed the three-sphere partition function of the theories, which implies that the theory is good/ugly/bad if k-N_1-N_2 is greater than/equal to/smaller than -1. In this paper we verify that this classification is consistent with the behavior of the superconformal index. We compar…
The aim of this paper is to clarify the relation between three different approaches of theories with a minimal length scale: A modification of the Lorentz-group in the 'Deformed Special Relativity', theories with a 'Generalized Uncertainty Principle' and those with 'Modified Dispersion Relations'. It is shown that the first two are equivalent, how they can be translated into each other, and how the third can be obtained from them. An adequate theory with a minimal length scale requires all three features to be present.
It has been proposed that the incorporation of an observer independent minimal length scale into the quantum field theories of the standard model effectively describes phenomenological aspects of quantum gravity. The aim of this paper is to interpret this description and its implications for scattering processes.
We show that the disc bulk one-point functions in a sl(n) Toda conformal field theory have a well-defined limit for the central charge c=n-1, and that their limiting values can be obtained from a limit of bulk one-point functions in the W_n minimal models. This comparison leads to a proposal for one-point functions for twisted boundary conditions in Toda theory.
We consider one dimensional lattice gauge theories constructed by the minimal coupling prescription. It is shown that these theories are exactly solvable in the thermodynamic limit. After considering the most general case, we discuss some special cases on finite lattices, and also work out some examples. There is no phase transition in these minimally coupled theories.
We present locally scale (Weyl) covariant generalisation of Minimal Massive Gravity theory using the language of exterior differential forms on Riemann-Cartan-Weyl space-times. The theory is expressed by a locally scale invariant action and locally scale covariant field equations are found by a first order variational formalism.
We study (p,q)=(2,4k) minimal superstrings within the minimal superstring field theory constructed in hep-th/0611045. We explicitly give a solution to the W_{1+\infty} constraints by using charged D-instanton operators, and show that the (m,n)-instanton sector with m positive-charged and n negative-charged ZZ-branes is described by an (m+n)\times (m+n) supermatrix model. We argue that the supermatrix model can be regarded as an open string field theory on the multi ZZ-brane system.
Generalized uncertainty relations are known to provide a minimal length $\hbar\sqrtβ$. The effect of such minimal length in the Casimir-Polder interactions between neutral atoms (molecules) is studied. The first order correction term in the minimal uncertainty parameter is derived and found to describe an attractive potential scaling as $r^{-9}$ as opposed to the well known $r^{-7}$ long range retarded potential.
The formulation of 2d-dilaton theories, like spherically reduced Einstein gravity, is greatly facilitated in a formulation as a first order theory with nonvanishing bosonic torsion. This is especially also true at the quantum level. The interpretation of superextensions as graded Poisson sigma models is found to cover generically all possible 2d supergravities. Superfields and thus superfluous auxiliary fields are avoided altogether. The procedure shows that generalizations of bosonic 2d models are highly ambiguous.
The reflection amplitudes in non-affine Toda theories which possess extended conformal symmetry are calculated. Considering affine Toda theories as perturbed non-affine Toda theories and using reflection relations which relate different fields with the same conformal dimension, we deduce the vacuum expectation values of local fields for all dual pairs of non-simply laced affine Toda field theories. As an application, we calculate the leading term in the short and long distance predictions of the two-point correlation functions in the massive phase of two coupled minimal models. The central cha…
We show that the introduction of a minimal length in the context of non-commutative spacetime gives rise (after some considerations) to higher-order theories. We then explicitly demonstrate how these higher-derivative theories appear as a generalization of the standard electromagnetism and general relativity by applying a consistent procedure that modifies the original Maxwell and Einstein-Hilbert actions. In order to set a bound on the minimal length, we compare the deviations from the inverse-square law with the potentials obtained in the higher-order theories and discuss the validity of the…
We discuss a two-dimensional lagrangian model with $N=2$ supersymmetry described by a Kähler potential $K(X,\bar{X})$ and superpotential $gX^k$ which explicitly exhibits renormalization group flows to infrared fixed points where the central charge has a value equal that of the $N=2$, $A_{k-1}$ minimal model. We consider the dressing of such models by N=2 supergravity: in contradistinction to bosonic or $N=1$ models, no modification of the $\b$-function takes place.
A general form for the equation of motion for higher-curvature gravity is obtained. The interesting feature of the analysis is that it can handle Lagrangians which contain non-minimal kinetic scalar couplings. Certain subtle features, which are absent for the Einstein-Hilbert term, arise in higher-curvature gravity. These are identified and an algorithmic prescription is presented for the evaluation of the generalized equation of motion.
There exists a natural $L_\infty$-algebra or $Q$-manifold that can be associated to any (gauge) field theory. Perturbatively, it can be obtained by reducing the $L_\infty$-algebra behind the jet space BV-BRST formulation to its minimal model. We explicitly construct the minimal models of self-dual Yang-Mills and self-dual gravity theories, which also represents their equations of motion as Free Differential Algebras. The minimal model regains all relevant information about the field theory, e.g. actions, charges, anomalies, can be understood in terms of the corresponding $Q$-cohomology.
We use the spinor helicity formalism in order to derive the dyadic forms for massless fields of various spins. We also give an iterated form of this approach in case higher spin theories are under study. This reduces calculations at hard and soft scattering problems in gauge theories drastically. Finally, we state and prove a theorem of gauge symmetry violation in the presence of minimal coupling with light in higher spin theories ($j>1/2$).
We obtain traversable wormhole and time machine solutions of the field equations of an alternative of gravity with non-minimally curvature-matter coupling. Our solutions exhibit a non-trivial redshift function and allow for matter that satisfy the dominant energy condition.
We describe the explicit construction of groves, the smallest gauge invariant classes of tree Feynman diagrams in gauge theories. The construction is valid for gauge theories with any number of group factors which may be mixed. It requires no summation over a complete gauge group multiplet of external matter fields. The method is therefore suitable for defining gauge invariant classes of Feynman diagrams for processes with many observed final state particles in the standard model and its extensions.
We classify the possible discrete (finite) symmetries of two--dimensional critical models described by unitary minimal conformally invariant theories. We find that all but six models have the group Z_2 as maximal symmetry. Among the six exceptional theories, four have no symmetry at all, while the other two are the familiar critical and tricritical 3--Potts models, which both have an S_3 symmetry. These symmetries are the expected ones, and coincide with the automorphism groups of the Dynkin diagrams of simply--laced simple Lie algebras ADE. We note that extended chiral algebras, when present,…
We construct free field representations of the $SW$-algebras SW(3/2,2) and SW(3/2,3/2,2) by using the corresponding Toda-Field-Theories. In constructing the series of minimal models using covariant vertex operators, we find a necessary restriction on the Cartan matrix of the Super-Lie-Algebra, also for the general case. Within this framework, this restriction claims that there be a minimum of one non-vanishing element on the diagonal of the Cartan matrix, which is without parallel in bosonic conformal field theory. As a consequence only two series of SSLA's yield minimal models, namely Osp(2n|…
Minimal BCOV theory is a classical field theory which describes a subclass of deformations of the category of perfect complexes on a Calabi-Yau variety. We compute minimal models for $L_\infty$-algebras describing minimal BCOV theory and its variants on flat space and find that they give certain $L_\infty$-extensions of the infinite-dimensional simple Lie superalgebra $\operatorname{SHO}(d|d)$. We apply this computation to compare an $\mathfrak{sl}_2$ action on an odd two-dimensional central extension of $\operatorname{SHO}(3|3)$ first discovered by Kac to an action of $\mathfrak{sl}_2$ on a v…
Quantum mechanical models with a minimal length are often described by modifying the commutation relation between position and momentum. Although this represents a small complication when described in momentum space, at least formally, the (quasi-)position representation acquires numerous issues, source of misunderstandings. In this work, we review these issues, clarifying some of the aspects of minimal length models, with particular reference to the representation of the position operator.
Mack has conjectured that all conformal field theories are equivalent to string theories. We explore the example of the two-dimensional minimal model CFTs and confirm that the Mellin transformed amplitudes have the desired properties of string theory in three-dimensional anti-de Sitter spacetime.
We show that a proposed duality [arXiv:0711.0054] between infinitely coupled gauge theories and superconformal field theories (SCFTs) with weakly gauged flavor groups predicts the existence of new rank 1 SCFTs. These superconformal fixed point theories have the same Coulomb branch singularities as the rank 1 E_6, E_7, and E_8 SCFTs, but have smaller flavor symmetry algebras and different central charges. Gauging various subalgebras of the flavor algebras of these rank 1 SCFTs provides many examples of infinite-coupling dualities, satisfying an intricate set of consistency checks. They also pro…
Integrable boundary conditions are studied for critical A-D-E and general graph-based lattice models of statistical mechanics. In particular, using techniques associated with the Temperley-Lieb algebra and fusion, a set of boundary Boltzmann weights which satisfies the boundary Yang-Baxter equation is obtained for each boundary condition. When appropriately specialized, these boundary weights, each of which depends on three spins, decompose into more natural two-spin edge weights. The specialized boundary conditions for the A-D-E cases are naturally in one-to-one correspondence with the confor…
It is discussed how a limiting procedure of (super)conformal field theories may result in logarithmic (super)conformal field theories. The construction is illustrated by logarithmic limits of (unitary) minimal models in conformal field theory and in N=1 superconformal field theory.
Gravitational waves in the presence of a non-minimal curvature-matter coupling are analysed, both in the Newman-Penrose and perturbation theory formalisms. Considering a cosmological constant as a source, the non-minimally coupled matter-curvature model reduces to $f(R)$ theories. This is in good agreement with the most recent data. Furthermore, a dark energy-like fluid is briefly considered, where the propagation equation for the tensor modes differs from the previous scenario, in that the scalar mode equation has an extra term, which can be interpreted as the longitudinal mode being the resu…
We study the gravitational production of heavy X-particles of mass of the order of the inflaton mass, produced after the end of inflation. We find that, in the presence of a derivative coupling of the inflaton field or of the X-field to the Einstein tensor, the number of gravitationally produced particles is suppressed as the strength of the coupling is increased.
We study the quasi-normal modes of asymptotically anti-de Sitter black holes in a class of shift-symmetric Horndeski theories where a gravitational scalar is derivatively coupled to the Einstein tensor. The space-time differs from exact Schwarzschild-anti-de Sitter, resulting in a different effective potential for the quasi-normal modes and a different spectrum. We numerically compute this spectrum for a massless test scalar coupled both minimally to the metric, and non-minimally to the gravitational scalar. We find interesting differences from the Schwarzschild-anti-de Sitter black hole found…
We study N=1,2,4 higher spin superalgebras in four dimensions and higher spin gauge theories based on them. We extend the existing minimal N=2,4 theories and find a minimal N=1 theory. Utilizing the basic structure of the minimal N=8 theory, we express the full field equations for the N=1,2,4 theories in a universal form without introducing Kleinian operators. We also use a non-minimal N=4 higher spin algebra tensored with U(3) to describe a higher spin extension of N=4 supergravity coupled to the massless vector multiplets arising in the KK spectrum of 11D supergravity on the N=3 supersymmetr…
The Coulomb branch indices of Argyres-Douglas theories on $L(k,1)\times S^{1}$ are recently identified with matrix elements of modular transforms of certain $2d$ vertex operator algebras in a particular limit. A one parameter generalization of the modular transformation matrices of $(2N+3,2)$ minimal models are proposed to compute the full Coulomb branch index of $(A_{1},A_{2N})$ Argyres-Douglas theories on the same space. Morever, M-theory construction of these theories suggests direct connection to the refined Chern-Simons theory. The connection is made precise by showing how the modular tra…
We present a systematic derivation for a general formula for the n-point coupling constant valid for affine Toda theories related to any simple Lie algebra {\bf g}. All n-point couplings with $n \geq 4$ are completely determined in terms of the masses and the three-point couplings. A general fusing rule, formulated in the root space of the Lie algebra, is derived for all n-point couplings.
A concise survey is given of the general method of reduction in the number of coupling parameters. Theories with several independent couplings are related to a set of theories with a single coupling. The reduced theories may or may not have particular symmetries. A few have asymptotic power series expansions, others contain non-integer powers and/or logarithmic factors. An example is given with two power series solutions, one with N = 2 Supersymmetry, and one with no known symmetry. In a second example, the reduced Yukawa coupling of the superpotential in a dual magnetic supersymmetric gauge t…
We study dynamics of two-dimensional N=(0,1) supersymmetric gauge theories. In particular, we propose that there is an infrared triality between certain triples of theories with orthogonal and symplectic gauge groups. The proposal is supported by matching of anomalies and elliptic genera. This triality can be viewed as a (0,1) counterpart of the (0,2) triality proposed earlier by two of the authors and A. Gadde. We also describe the relation between global anomalies in gauge theoretic and sigma-model descriptions, filling in a gap in the present literature.
We give a recipe relating holomorphic quantities in supersymmetric field theory to their descendants in non-supersymmetric Z_2 orbifold field theories. This recipe, consistent with a recent proposal of Strassler, gives exact results for bifermion condensates, domain wall tensions and gauge coupling constants in the planar limit of the orbifold theories.
A large class of two-dimensional dilaton-gravity theories in asymptotically AdS$_2$ spacetimes are holographically dual to a matrix integral, interpreted as an ensemble average over Hamiltonians. Viewing these theories as Jackiw-Teitelboim gravity with a gas of defects, we extend this duality to a broader class of dilaton potentials compared to previous work by including conical defects with small deficit angles. In order to do this we show that these theories are equal to the large $p$ limit of a natural deformation of the $(2,p)$ minimal string theory.
There exists a unique class of local Higher Spin Gravities with propagating massless fields in $4d$ - Chiral Higher Spin Gravity. Originally, it was formulated in the light-cone gauge. We construct a covariant form of this theory as a Free Differential Algebra up to NLO, i.e. at the level of equations of motion. It also contains the recently discovered covariant forms of the higher spin extensions of SDYM and SDGR, as well as SDYM and SDGR themselves. From the mathematical viewpoint the result is equivalent to taking the minimal model (in the sense of $L_\infty$-algebras) of the jet-space exte…
An evidence for nontriviality of asymptotically non-free (ANF) Yang-Mills theories is found on the basis of optimized perturbation theory. It is argued that these theories with matter couplings can be made nontrivial by means of the reduction of couplings, leading to the idea of dynamical unification of couplings (DUC) The second-order reduction of couplings in the ANF $SU(3)$-gauged Higgs-Yukawa theory, which is assumed to be nontrivial here, is carried out to motivate independent investigations on its nontriviality and DUC.
We study theories of gravity with non-minimal coupling between polarized media with pole-dipole and quadrupole moments and an arbitrary function of the space-time curvature scalar $R$ and the squares of the Ricci and Riemann curvature tensors. We obtain the general form of the equation of motion and show that an induced quadrupole moment emerges as a result of the curvature tensor dependence of the function coupled to the matter. We derive the explicit forms of the equations of motion in the particular cases of coupling to a function of the curvature scalar alone, coupling to an arbitrary func…
We study a large family of metric-affine theories with a projective symmetry, including non-minimally coupled matter fields which respect this invariance. The symmetry is straightforwardly realised by imposing that the connection only enters through the symmetric part of the Ricci tensor, even in the matter sector. We leave the connection completely free (including torsion) and obtain its general solution as the Levi-Civita connection of an auxiliary metric, showing that the torsion only appears as a projective mode. This result justifies the widely used condition of setting vanishing torsion …
We construct a class of theories with 16 supersymmetries on spheres of dimension nine and less. The gauge coupling and mass terms for the scalar fields depend on the polar angle away from the north pole. Assuming finite coupling on the north pole, this leads to zero coupling at the south pole for $d>4$ and infinite coupling at the south pole for $d<4$. The underlying supersymmetry algebra of these theories is shown to be isomorphic to the Poincaré superalgebra in $d$-dimensions. We also give a localization procedure which leads to nontrivial results for $d=2$.
We argue that the topology of the quantum coupling space and the low energy effective action on the Coulomb branch of scale invariant N=2 SU(n) gauge theories pick out a preferred nonperturbative definition of the gauge coupling up to non-singular holomorphic reparametrizations.
The self-consistent matter coupling is found in a broad class of minimally modified gravity theories which was discovered recently. All constraints in the theories remain first class and thus a graviton has only 2 local degrees of freedom. The cosmological solution of one of the examples in this class, the so-called square root gravity, exhibits a singularity freeness at high energy limit. At low energy limit, the theory smoothly connects to GR. A general feature of the theories in this class, with the self-consistent matter coupling discovered in our current work, is the non-trivial interacti…
We describe a general way of constructing integrable defect theories as perturbations of conformal field theory by local defect operators. The method relies on folding the system onto a boundary field theory of twice the central charge. The classification of integrable defect theories obtained in this way parallels that of integrable bulk theories which are a perturbation of the tensor product of two conformal field theories. These include local defect perturbations of all $c<1$ minimal models, as well as of the coset theories based on SO(2n), obtained in this way. We discuss in detail the for…
We investigate the strong coupling limit of a family of Chern-Simons-matter theories in the planar limit. The family consists of ${\cal N}=3$ theories with the gauge group ${\rm U}(N_1)_{k_1}\times{\rm U}(N_2)_{k_2}$ coupled to $n$ bi-fundamental hypermultiplets. All observables which can be determined from the planar resolvent turn out to have finite limits in the large 't Hooft coupling limit. Possible gravity duals are briefly discussed. We observe that Kac-Moody algebras govern the structure of the planar spectral curves of the theories.
p-form gauge theories with Stueckelberg coupling are quantized in an irreducible antifield-BRST way. As a consequence, neither the ghosts of ghosts nor their antifields appear. Some irreducible gauge conditions are inferred naturally within our formalism. In the end we briefly discuss the interacting case.
