We propose a scenario of gauge-string correspondence by relating the SU(3) colour group to hidden space-time isometries originating from extra dimensions. These isometries ($α$-symmetries) are the special symmetries of RNS superstring theories under global non-linear space-time transformations. The vertex operators for the octet of gluons are constructed by the procedure of ``photon painting'', that is, with the SU(3) subgroup of the $α$-symmetry generators acting on a regular open string photon, so the corresponding open string excitations are in the adjoint of SU(3). Remarkably, the operator algebra of these massless gluon vertices is closed and possesses the full zigzag symmetry, crucial for the isomorphism between open strings and QCD. As a result, the scattering amplitudes of the constructed open string vertex operators have a field-theoretic rather than a stringy structure, including the absense of standard tower of massive intermediate states.Our model also suggests that the total number of underlying hidden dimensions is three, with each extra dimension carrying its appropriate SU(3) colour and anticolour.
We formulate the field equations for $SU(\infty)$ Einstein-Yang-Mills theory, and find spherically symmetric black-hole solutions. This model may be motivated by string theory considerations, given the enormous gauge symmetries which characterize string theory. The solutions simplify considerably in the presence of a negative cosmological constant, particularly for the limiting cases of a very large cosmological constant or very small gauge field. The situation of an arbitrarily small gauge field is relevant for holography and we comment on the AdS/CFT conjecture in this light. The black holes…
It is shown that local symmetry transformations of the maximal AdS supergravity in seven-dimensional anti de Sitter space induce those of the N=(2,0) conformal supergravity on the six-dimensional boundary at infinity. Boundary values of the AdS supergravity fields form a supermultiplet of the conformal supergravity.
We study the breaking of baryonic symmetries in the AdS_5/CFT_4 correspondence for D3 branes at Calabi-Yau three-fold singularities. This leads, for particular VEVs, to the emergence of non-anomalous baryonic symmetries during the renormalization group flow. We claim that these VEVs correspond to critical values of the B-field moduli in the dual supergravity backgrounds. We study in detail the C^3/Z_3 orbifold, the cone over F_0 and the C^3/Z_5 orbifold. For the first two examples, we study the dual supergravity backgrounds that correspond to the breaking of the emerging baryonic symmetries an…
We calculate the superconformal indices of a class of six-dimensional ${\cal N}=(1,0)$ superconformal field theories realized on M5-branes at $\mathbb{C}^2/\mathbb{Z}_k$ singularity by using the method developed in previous works of the authors and collaborators. We use the AdS/CFT correspondence, and finite $N$ corrections are included as the contribution of M2-branes wrapped on two-cycles in $S^4/\mathbb{Z}_k$. We confirm that the indices are consistent with the expected flavor symmetries.
By incorporating higher-form symmetries, we propose a refined definition of the theories obtained by compactification of the 6d $(2,0)$ theory on a three-manifold $M_3$. This generalization is applicable to both the 3d $\mathcal{N}=2$ and $\mathcal{N}=1$ supersymmetric reductions. An observable that is sensitive to the higher-form symmetries is the Witten index, which can be computed by counting solutions to a set of Bethe equations that are determined by $M_3$. This is carried out in detail for $M_3$ a Seifert manifold, where we compute a refined version of the Witten index. In the context of…
We study U(1) symmetries dual to Betti multiplets in the AdS_4/CFT_3 correspondence for M2 branes at Calabi-Yau four-fold singularities. Analysis of the boundary conditions for vector fields in AdS_4 allows for a choice where wrapped M5 brane states carrying non-zero charge under such symmetries can be considered. We begin by focusing on isolated toric singularities without vanishing six-cycles, and study in detail the cone over Q^{111}. The boundary conditions considered are dual to a CFT where the gauge group is U(1)^2 x SU(N)^4. We find agreement between the spectrum of gauge-invariant bary…
Colour $SU(3)$ group is an exact symmetry of Quantum Chromodynamics, which describes strong interactions between quarks and gluons. Supplemented by two internal symmetries, $SU(2)$ and $U(1)$, it serves as the internal symmetry of the Standard Model, describing as well the electroweak interactions of quarks and leptons. The colour$SU(3)$ symmetry is exact, while two other symmetries are broken by means of the Higgs-Kibble mechanism. The three colours and fractional quarks charges with values $1/3$ and $2/3$ suggest that the cyclic group $Z_3$ may play a crucial role in quark field dynamics. In…
We study new symmetries between A and D type quiver gauge theories with different numbers of colors. We realize these gauge theories with twisted masses via a brane construction that reproduces all the parameters of the Gauge/Bethe correspondence.
We study theories with W-algebra symmetries and their relation to WZNW models on (super-)groups. Correlation functions of the WZNW models are expressed in terms of correlators of CFTs with W-algebra symmetry. The symmetries of the theories involved in these correspondences are related by the Drinfeld-Sokolov reduction of Lie algebras to W-algebras. The W-algebras considered in this paper are the Bershadsky-Polyakov algebra for sl(3) and the quasi-superconformal algebra for generic sl(N|M). The quantum W-algebras obtained from affine sl(N) are constructed using embeddings of sl(2) into sl(N), a…
In the first part of this thesis we study baryonic U(1) symmetries dual to Betti multiplets in the AdS_4/CFT_3 correspondence for M2 branes at Calabi-Yau 4-fold singularities. We begin by focusing on isolated toric singularities without vanishing 6-cycles, which we classify, and propose for them field theory duals. We then study in detail the cone over Q^111 and find agreement between the spectrum of baryonic operators in this theory and M5 branes wrapping 5-cycles in the Q^111 space. The physics of vacua in which these symmetries are spontaneously broken precisely matches a dual gravity analy…
According to the Hamiltonian formalism, nonrelativistic phase space may be considered as an arena of physics, with momentum and position treated as independent variables. Invariance of x^2+p^2 constitutes then a natural generalization of ordinary rotational invariance. We consider Dirac-like linearization of this form, with position and momentum satisfying standard commutation relations. This leads to the identification of a quantum-level structure from which some phase space properties might emerge. Genuine rotations and reflections in phase space are tied to the existence of new quantum numb…
We explain how to achieve the traceless gauge for the spatial part of the spin connection in the framework of the recently proposed correspondence between the (appropriately truncated) bosonic sectors of maximal supergravities and the `geodesic' sigma-model over E10/K(E10) at low levels. After making this gauge choice, the residual symmetries on both sides of this correspondence match precisely. The gauge choice also allows us to give a physical interpretation to the multiplicity of certain primitive affine null roots of E10.
It is usually assumed that the proton stability requires the coloured triplet partner of the electroweak Higgs doublet to be superheavy (with a mass $\sim M_{GUT}$). We show that this is a very model-dependent statement and the colour triplet can be as light as the weak doublet without leading to the proton decay problem: instead of using the mass difference the splitting can occur between the doublet and triplet Yukawa coupling constants. In this scenario the GUT symmetry breaking automatically induces an extremely strong suppression $\sim M_W/M_{GUT}$ of the coloured Higgs effective Yukawa c…
We provide a realization of the AdS$_2$/CFT$_1$ correspondence in terms of asymptotic symmetries of the AdS$_2\times$S$^1$ and AdS$_2\times$S$^2$ geometries arising in near-extremal BTZ and Reissner-Nordström black holes. Cardy's formula exactly accounts for the deviation of the Bekenstein-Hawking entropy from extremality. We also argue that this result can be extended to more general black holes near extremality.
It is widely believed that consistent theories of quantum gravity satisfy two basic kinematic constraints: they are free from any global symmetry, and they contain a complete spectrum of gauge charges. For compact, abelian gauge groups, completeness follows from the absence of a 1-form global symmetry. However, this correspondence breaks down for more general gauge groups, where the breaking of the 1-form symmetry is insufficient to guarantee a complete spectrum. We show that the correspondence may be restored by broadening our notion of symmetry to include non-invertible topological operators…
We derive a series of quantitative bulk-boundary correspondences for 3D bosonic and fermionic symmetry-protected topological (SPT) phases under the assumption that the surface is gapped, symmetric and topologically ordered, i.e., a symmetry-enriched topological (SET) state. We consider those SPT phases that are protected by the mirror symmetry and continuous symmetries that form a group of $U(1)$, $SU(2)$ or $SO(3)$. In particular, the fermionic cases correspond to a crystalline version of 3D topological insulators and topological superconductors in the famous ten-fold-way classification, with…
The full list of conserved conformal higher spin currents built from massless scalar and spinor fields is presented. It is shown that, analogously to the relationship between usual conformal and AdS symmetries, the set of the conformal higher spin symmetry parameters associated with the conformal conserved currents in d dimensions is in the one-to-one correspondence with the result of the dimensional reduction of the usual (i.e., non-conformal) higher spin symmetry parameters in d+1 dimensions.
The covariant form of the field equations for two--dimensional $R^2$--gravity with torsion as well as its Hamiltonian formulation are shown to suggest the choice of the light--cone gauge. Further a one--to--one correspondence between the Hamiltonian gauge symmetries and the diffeomorphisms and local Lorentz transformations is established, thus proving that there are no hidden local symmetries responsible for the complete integrability of the model. Finally the constraint algebra is shown to have no quantum anomalies so that Dirac's quantization should be applicable.
It has been conjectured that a near-extreme Kerr black hole is described by a 2d CFT. Previous work has shown that CFT operators dual to axisymmetric gravitational perturbations have integer conformal weights. In this paper, we study the analogous problem in 5d. We consider the most general near-extreme vacuum black hole with two rotational symmetries. This includes Myers-Perry black holes, black rings and Kaluza-Klein black holes. We find that operators dual to gravitational (or electromagnetic or massless scalar field) perturbations preserving both rotational symmetries have integer conforma…
We present a detailed discussion of the duality between dilaton gravity on AdS_2 and open strings. The correspondence between the two theories is established using their symmetries and field theoretical, thermodynamic, and statistical arguments. We use the dual conformal field theory to describe two-dimensional black holes. In particular, all the semiclassical features of the black holes, including the entropy, have a natural interpretation in terms of the dual microscopic conformal dynamics. The previous results are discussed in the general framework of the Anti-de Sitter/Conformal Field Theo…
We study the correspondence between the linear matrix model and the interacting nonlinear string theory. Starting from the simple matrix harmonic oscillator states, we derive in a direct way scattering amplitudes of 2-dimensional strings, exhibiting the nonlinear equation generating arbitrary N-point tree amplitudes. An even closer connection between the matrix model and the conformal string theory is seen in studies of the symmetry algebra of the system.
Using the AdS/CFT correspondence, we identify the symmetry algebra of the Laplacian on Euclidean space as an explicit quotient of the universal enveloping algebra of the Lie algebra of conformal motions. We construct analogues of these symmetries on a general conformal manifold.
The asymptotic symmetries of the near-horizon geometry of a lifted (near-extremal) Reissner-Nordstrom black hole, obtained by inverting the Kaluza-Klein reduction, explain the deviation of the Bekenstein-Hawking entropy from extremality. We point out the fact that the extra dimension allows us to justify the use of a Virasoro mode decomposition along the time-like boundary of the near-horizon geometry, AdS$_2\times$S$^n$, of the lower-dimensional (Reissner-Nordstrom) spacetime.
We investigate symmetries of the six-dimensional $(2,0)$ theory reduced along a compact null direction. The action for this theory was deduced by considering M-theory on $AdS_7 \times S^4$ and reducing the $AdS_7$ factor along a time-like Hopf fibration which breaks one quarter of the supersymmetry and reduces the isometry group from $SO(6,2)$ to $SU(3,1)$. The boundary theory was previously shown to have 24 supercharges and a Lifshitz scaling symmetry. In this paper, we show that it has four boost-like symmetries and an additional conformal symmetry which furnish a representation of $SU(3,1)$…
We prove that the finite gauge transformation of the Ramond sector of the modified cubic superstring field theory is ill-defined due to collisions of picture changing operators. Despite this problem we study to what extent could a bijective classical correspondence between this theory and the (presumably consistent) non-polynomial theory exist. We find that the classical equivalence between these two theories can almost be extended to the Ramond sector: We construct mappings between the string fields (NS and Ramond, including Chan-Paton factors and the various GSO sectors) of the two theories …
A new Lagrangian description that interpolates between the Nambu--Goto and Polyakov version of interacting strings is given. Certain essential modifications in the Poission bracket structure of this interpolating theory generates noncommutativity among the string coordinates for both free and interacting strings. The noncommutativity is shown to be a direct consequence of the nontrivial boundary conditions. A thorough analysis of the gauge symmetry is presented taking into account the new modified constraint algebra, which follows from the noncommutative structures and finally a smooth corresp…
We discuss infinite-dimensional hidden symmetry algebras (and hence an infinite number of conserved nonlocal charges) of the N-extented self-dual super Yang-Mills equations for general N\leq4 by using the supertwistor correspondence. Furthermore, by enhancing the supertwistor space, we construct the N-extended self-dual super Yang-Mills hierarchies, which describe infinite sets of graded Abelian symmetries. We also show that the open topological B-model with the enhanced supertwistor space as target manifold will describe the hierarchies. Furthermore, these hierarchies will in turn -- by a sup…
In this paper, we study the correspondence between a field theory in de Sitter space in $D$-dimensions and a dual conformal field theory in a euclidean space in $(D-1)$-dimensions. In particular, we investigate the form in which this correspondence is established for a system of interacting scalar and a vector fields propagating in de Sitter space. We analyze some necessary (but not sufficient) conditions for which conformal symmetry is preserved in the dual theory in $(D-1)$-dimensions, making possible the establishment of the correspondence. The discussion that we address on this paper is fr…
In these lecture notes we first assemble the basic ingredients of supersymmetric gauge theories (particularly N=4 super-Yang-Mills theory), supergravity, and superstring theory. Brane solutions are surveyed. The geometry and symmetries of anti-de Sitter space are discussed. The AdS/CFT correspondence of Maldacena and its application to correlation functions in the the conformal phase of N=4 SYM are explained in considerable detail. A pedagogical treatment of holographic RG flows is given including a review of the conformal anomaly in four-dimensional quantum field theory and its calculation fr…
We propose two different high-energy-theory correspondences with graphene (and related materials) scenarios, associated to grain boundaries, that are topological defects for which both Dirac points are necessary. The first correspondence points to a $(3+1)$-dimensional theory, with nonzero torsion, with spatiotemporal gauge group $SO(3,1)$, locally isomorphic to the Lorentz group in $(3+1)$ dimensions, or to the de Sitter group in $(2+1)$ dimensions. The other correspondence treats the two Dirac fields as an internal symmetry doublet, and it is linked here with unconventional supersymmetry wit…
We study conformal symmetries on the horizon of a general stationary and axisymmetric black hole. We find that there exist physically reasonable boundary conditions that uniquely determine a set of symmetry generators, which form one copy of the Virasoro algebra. For extremal black holes, Cardy's formula reproduces exactly the Bekenstein-Hawking entropy.
Free string theory on the plane-wave background displays a discrete Z2 symmetry exchanging the two transverse SO(4) rotation groups. This symmetry should be respected also at the interacting level. We show that the zero mode structure proposed in hep-th/0208148 can be completed to a full kinematical vertex, contrary to claims appeared in the previous literature. We also comment on the relation with recent works on the string-bit formalism and on the comparison with the field theory side of the correspondence.
In the current version of QCD the quarks are described by ordinary Dirac fields, organized in the following internal symmetry multiplets: the $SU(3)$ colour, the $SU(2)$ flavour, and broken $SU(3)$ providing the family triplets. \noindent In this paper we argue that internal and external (i.e. space-time) symmetries are entangled at least in the colour sector in order to introduce the spinorial quark fields in a way providing all the internal quark's degrees of freedom which do appear in the Standard Model. Because the $SU(3)$ colour algebra is endowed with natural $Z_3$-graded discrete automo…
We discuss the gravity dual description for a non-commutative Yang-Mills theory, which reduces to that on AdS_{5} x S_{5} in the commutative limit. It is found that doubletons do not decouple in this dual gravity description unless one takes the commutative limit. The decoupling of the doubletons in AdS_{5} space implies that the dual gauge theory has SU(N) gauge symmetry. Our result implies that this gravity description is dual to non-commutative U(N) gauge theory. It is compatible with the claim that U(1) and SU(N) gauge symmetries can not separate in non-commutative U(N) gauge theory.
We study symmetries of quantum field theories involving topologically distinct sectors of the field space. To exhibit these symmetries we define special gauge invariant observables, which we call the $qq$-characters. In the context of the BPS/CFT correspondence, using these observables, we derive an infinite set of Dyson-Schwinger-type relations. These relations imply that the supersymmetric partition functions in the presence of $Ω$-deformation and defects obey the Ward identities of two dimensional conformal field theory and its $q$-deformations. The details will be discussed in the companio…
Non-trivial K-theory groups and non-trivial cobordism groups can lead to global symmetries which are conjectured to be absent in quantum gravity. Inspired by open-closed string duality, we propose a correspondence between the two groups, which can be considered as the physical manifestation of a generalisation of the classic Conner--Floyd isomorphism. The picture is exemplified by the relations between KO-groups and Spin-cobordisms and between K-groups and Spin$^c$-cobordisms. Global symmetries related by such isomorphism are eventually gauged. By combining K-theory and cobordism, we recover t…
We study four dimensional N=1 gauge theories that arise on the worldvolume of D3-branes probing complex cones over del Pezzo surfaces. Global symmetries of the gauge theories are made explicit by using a correspondence between bifundamental fields in the quivers and divisors in the underlying geometry. These global symmetries are hidden, being unbroken when all inverse gauge couplings of the quiver theory vanish. In the broken phase, for finite gauge couplings, only the Cartan subalgebra is manifest as a global symmetry. Superpotentials for these models are constructed using global symmetry in…
We find a surprising connection between asymptotically flat space-times and non-relativistic conformal systems in one lower dimension. The BMS group is the group of asymptotic isometries of flat Minkowski space at null infinity. This is known to be infinite dimensional in three and four dimensions. We show that the BMS algebra in 3 dimensions is the same as the 2D Galilean Conformal Algebra which is of relevance to non-relativistic conformal symmetries. We further justify our proposal by looking at a Penrose limit of a radially infalling null ray inspired by non-relativistic scaling and obtain…
We determine the gauge symmetries of all p-forms in maximal three-dimensional gauged supergravity by requiring invariance of the Lagrangian. It is shown that in a particular ungauged limit these symmetries are in precise correspondence to those predicted by the very-extended Kac-Moody algebra E11. We demonstrate that whereas in the ungauged limit the bosonic gauge algebra closes off-shell, the closure is only on-shell in the full gauged theory. This underlines the importance of dynamics for understanding the Kac-Moody origin of the symmetries of gauged supergravity.
Using BRST-BV formulation of relativistic dynamics, arbitrary spin massless and massive field propagating in flat space and arbitrary spin massless fields propagating in AdS space are considered. For such fields, BRST-BV Lagrangians invariant under gauge transformations are obtained. The Lagrangians and gauge transformations are built in terms of traceless gauge fields and traceless gauge transformation parameters. The use of the Poincare parametrization of AdS space allows us to get simple BRST-BV Lagrangian for AdS fields. By imposing the Siegel gauge condition, we get gauge-fixed Lagrangian…
We calculate partition function and correlation functions in A-twisted 2d $\mathcal{N}=(2,2)$ theories and topologically twisted 3d $\mathcal{N}=2$ theories containing adjoint chiral multiplet with particular choices of $R$-charges and the magnetic fluxes for flavor symmetries. According to Gauge-Bethe correspondence, they correspond to Heisenberg XXX and XXZ spin chain models. We identify the partition function as the inverse of the norm of the Bethe eigenstates. Correlation functions are identified as the coefficients of the expectation value of Baxter $Q$-operators. In addition, we consider…
In this letter we use the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence to establish a set of old conjectures about symmetries in quantum gravity. These are that no global symmetries are possible, that internal gauge symmetries must come with dynamical objects that transform in all irreducible representations, and that internal gauge groups must be compact. These conjectures are not obviously true from a bulk perspective, they are nontrivial consequences of the non-perturbative consistency of the correspondence. More details of and background for these arguments are presented …
The focus of the present thesis is on the analysis of gauge symmetry and its various impacts on gauge theories. In the first part of this thesis, we have studied different aspects of symmetries in connection with various field and string theoretic models. The manifestations of gauge symmetries and their interconnection with the diffeomorphism invariances have been discussed in the context of different generally covariant models like string, membrane, $p-$brane and metric gravity. Analysis of interacting string with proper inclusion of the stringy boundary conditions led to the noncommutative n…
We study the two-dimensional twisted (0,2) sigma-model on various smooth complex flag manifolds G/B, and explore its relevance to the geometric Langlands program. We find that an equivalence - at the level of the holomorphic chiral algebra - between a bosonic string on G/B and a B-gauged version of itself on G, will imply an isomorphism of classical W-algebras and a level relation which underlie a geometric Langlands correspondence for G=SL(N,C). This furnishes an alternative physical interpretation of the geometric Langlands correspondence for G=SL(N,C), to that demonstrated earlier by Kapust…
We investigate asymptotic symmetries in flat backgrounds of dimension higher than or equal to four. For spin two we provide the counterpart of the extended BMS transformations found by Campiglia and Laddha in four-dimensional Minkowski space. We then identify higher-spin supertranslations and generalised superrotations in any dimension. These symmetries are in one-to-one correspondence with spin-$s$ partially-massless representations on the celestial sphere, with supertranslations corresponding in particular to the representations with maximal depth. We discuss the definition of the correspond…
Field theories in black hole spacetimes undergo dimensional reduction near horizon (in the Rindler limit) to two dimensional conformal field theories. We investigate this enhancement of symmetries in the context of gauge/gravity duality by considering Rindler space as boundary of Anti-de Sitter space in three spacetime dimensions. We show that the loxodromy conjugacy class of the SO(2,2) isometry group is responsible for generating the special conformal transformations on the boundary under RG flow. We use this approach to present an alternative derivation of the two-point function in Rindler …
Hidden theories coupled to the SM may provide emergent (dark) vectors, that are composites/bound-states of the hidden fields. This is motivated by paradigms emerging from the AdS/CFT correspondence but it is a more general phenomenon. We explore the general setup and find that UV interactions among currents or charged fields give rise to emergent vectors in the IR. We study the general properties of such vectors and argue that they can be generically different from fundamental dark photons that have been studied so far.
After a review of symmetries and classical solutions involved in the AdS3/CFT2 correspondence, we apply a similar analysis to asymptotically flat spacetimes at null infinity in 3 and 4 dimensions. In the spirit of two dimensional conformal field theory, the symmetry algebra of asymptotically flat spacetimes at null infinity in 4 dimensions is taken to be the semi-direct sum of supertranslations with infinitesimal local conformal transformations and not, as usually done, with the Lorentz algebra. As a first application, we derive how the symmetry algebra is realized on solution space. In partic…
We generalise the analysis carried out in [arXiv:0710.5796], and find that our previous results can be extended beyond the case of SL(N,C). In particular, we show that an equivalence--at the level of the holomorphic chiral algebra--between a bosonic string on a smooth coset manifold G/B and a B-gauged version of itself on G, will imply an isomorphism of classical W-algebras and a level relation which underlie a geometric Langlands correspondence for the simply-laced, complex ADE-groups. In addition, as opposed to line operators and branes of an open topological sigma-model, the Hecke operators…
Spinor structure and internal symmetries are considered within one theoretical framework based on the generalized spin and abstract Hilbert space. Complex momentum is understood as a generating kernel of the underlying spinor structure. It is shown that tensor products of biquaternion algebras are associated with the each irreducible representation of the Lorentz group. Space-time discrete symmetries $P$, $T$ and their combination $PT$ are generated by the fundamental automorphisms of this algebraic background (Clifford algebras). Charge conjugation $C$ is presented by a pseudoautomorphism of …
Using the concept of variational tricomplex endowed with a presymplectic structure, we formulate the general notion of symmetry. We show that each generalized symmetry of a gauge system gives rise to a sequence of conservation laws that are represented by on-shell closed forms of various degrees. This extends the usual Noether's correspondence between global symmetries and conservation laws to the case of lower-degree conservation laws and not necessarily variational equations of motion. Finally, we equip the space of conservation laws of a given degree with a Lie bracket and establish a homom…
