Relying solely on unitarity and the consistency with large-distance black hole physics, we derive model-independent properties of the microscopic black holes and of short-distance gravity in theories with N particle species. In this class of theories black holes can be as light as M_{Planck}/\sqrt{N} and be produced in particle collisions above this energy. We show, that the micro black holes must come in the same variety as the species do, although their label is not associated with any conserved charge measurable at large distances. In contrast with big Schwarzschildian ones, the evaporation of the smallest black holes is maximally undemocratic and is biased in favor of particular species. With an increasing mass the democracy characteristic to the usual macro black holes is gradually regained. The lowest possible mass above which black holes become Einsteinian is \sqrt{N} M_{Planck}. This fact uncovers the new fundamental scale (below the quantum gravity scale) above which gravity changes classically, and the properties of black holes and gravity are such as if some extra dimensions open up, although no such input exists in the theory. Our observations indicate that geometry of space may be an emergent concept following from large number of species and the consistency with macro black hole physics. We apply our findings to the phenomenological properties of the micro black holes that can be observed at LHC for large N. Extrapolating our findings to small N, one may ask whether the existence of quark and lepton flavors is already an evidence for emergent extra dimensions at short distances.
We address the question how string compactifications with D-branes are consistent with the black hole bound, which arises in any theory with number of particle species to which the black holes can evaporate. For the Kaluza-Klein particles, both longitudinal and transversal to the D-branes, it is relatively easy to see that the black hole bound is saturated, and the geometric relations can be understood in the language of species-counting. We next address the question of the black hole evaporation into the higher string states and discover, that contrary to the naive intuition, the exponentiall…
We study the low-energy effective theory in N=2 super Yang-Mills theories by microscopic and exact approaches. We calculate the one-instanton correction to the prepotential for any simple Lie group from the microscopic approach. We also study the Picard-Fuchs equations and their solutions in the semi- classical regime for classical gauge groups with rank r \leq 3. We find that for gauge groups G=A_r, B_r, C_r (r \leq 3) the microscopic results agree with those from the exact solutions.
We show that lowering of the gravitational cutoff relative to the Planck mass, imposed by black hole physics in theories with N species, has an independent justification from quantum information theory. First, this scale marks the limiting capacity of any information processor. Secondly, by taking into the account the limitations of the quantum information storage in any system with species, the bound on the gravity cutoff becomes equivalent to the holographic bound, and this equivalence automatically implies the equality of entanglement and Bekenstein-Hawking entropies. Next, the same bound f…
In this note, we solve an extended version of the N=1 super Yang-Mills theory with gauge group U(N), an adjoint chiral multiplet and Nf flavors of quarks, by using the N=1 microscopic formalism based on Nekrasov's sums over colored partitions. Our main new result is the computation of the general mesonic operators. We prove that the generalized Konishi anomaly equations with flavors are satisfied at the non-perturbative level. This yields in particular a microscopic, first principle derivation of the matrix model disk diagram contributions that must be included in the Dijkgraaf-Vafa approach.
Several distinct mechanisms of confinement and dynamical symmetry breaking (DSB) are identified, in a class of supersymmetric $SU(n_c)$, $USp(2n_c)$ and $SO(n_c)$ gauge theories. In some of the vacua, the magnetic monopoles carrying nontrivial flavor quantum numbers condense, causing confinement and symmetry breaking simultaneously. In more general classes of vacua, however, the effective low-energy degrees of freedom are found to be constituents of the monopoles - dual (magnetic) quarks. These magnetic quarks condense and give rise to confinement and DSB. We find two more important classes of…
We consider the N=1 super Yang-Mills theory with gauge group U(N), adjoint chiral multiplet X and tree-level superpotential Tr W(X). We compute the quantum effective superpotential W_mic as a function of arbitrary off-shell boundary conditions at infinity for the scalar field X. This effective superpotential has a remarkable property: its critical points are in one-to-one correspondence with the full set of quantum vacua of the theory, providing in particular a unified picture of solutions with different ranks for the low energy gauge group. In this sense, W_mic is a good microscopic effective…
We explain how to generalize Nekrasov's microscopic approach to N=2 gauge theories to the N=1 case, focusing on the typical example of the U(N) theory with one adjoint chiral multiplet X and an arbitrary polynomial tree-level superpotential Tr W(X). We provide a detailed analysis of the generalized glueball operators and a non-perturbative discussion of the Dijkgraaf-Vafa matrix model and of the generalized Konishi anomaly equations. We compute in particular the non-trivial quantum corrections to the Virasoro operators and algebra that generate these equations. We have performed explicit calcu…
We consider unitary and weakly coupled theories of gravity that extend Einstein gravity and reduce to it asymptotically at large distances. Our discussion is restricted to such theories that, similarly to Einstein gravity, contain black holes as semiclassical states in a range of scales. We show that, at a given scale, the entropy of these black holes has to be larger than the number of elementary light species in the theory. Our bound follows from the observation that the black hole entropy has to be larger than the product of its mass and horizon radius (in units of Planck's constant divided…
We give a brief account of the recent progresses in super Yang-Mills theories based in particular on the application of Nekrasov's instanton technology to the case of N=1 supersymmetry. We have developed a first-principle formalism from which any chiral observable in the theory can be computed, including in strongly coupled confining vacua. The correlators are first expressed in terms of some external variables as sums over colored partitions. The external variables are then fixed to their physical values by extremizing the microscopic quantum superpotential. Remarquably, the results can be sh…
In theories with many copies of the Standard Model virtual black hole exchange may produce effective higher dimensional operators that can be treated below the cutoff scale as fundamental vertices of interspecies non-gravitational interaction. We consider the vertex that couples fermions of one species through magnetic moment to photons of other species, and study the quantum corrections it generates. In particular, we find kinetic mixing between photons of different species produced via fermion loops. Diagonalization of gauge kinetic terms then renders the fermions millicharged under other sp…
Unitarity implies that the evaporation of microscopic quasi-classical black holes cannot be universal in different particle species. This creates a puzzle, since it conflicts with the thermal nature of quasi-classical black holes, according to which all the species should see the same horizon and be produced with the same Hawking temperatures. We resolve this puzzle by showing that for the microscopic black holes, on top the usual quantum evaporation time, there is a new time-scale which characterizes a purely classical process during which the black hole looses the ability to differentiate am…
Following a recent conjecture by Lapan, Simons and Strominger, we revisit and discuss an intrinsically heterotic class of conformal field theories, emphasizing their Lagrangian construction as asymmetrically gauged WZW models, which may be useful in several applications to the study of supersymmetric strings and black holes in heterotic and type II string theory compactified on T^6 and K3 X T^2 respectively. In these cases, the leading supergravity geometry is singular, but higher order corrections remove this singularity in a way that is consistent with, for example the non-zero entropy for t…
Affine Toda theory is a relativistic integrable theory in two dimensions possessing solutions describing a number of different species of solitons when the coupling is chosen to be imaginary. These nevertheless carry real energy and momentum. To each species of soliton there has to correspond an antisoliton species. There are two different ways of realising the antisoliton whose equivalence is shown to follow from a surprising identity satisfied within the underlying affine Kac-Moody group. This is the classical analogue of the crossing property of analytic S-matrix theory. Since a complex par…
We conjecture an intrinsic UV cutoff for the validity of the effective field theory with a large number of species coupled to gravity. In four dimensions such a UV cutoff takes the form $Λ=\sqrt{λ/ N}M_p$ for $N$ scalar fields with the same potential $λϕ_i^4$, $i=1,...,N$. This conjecture implies that the assisted chaotic inflation or N-flation might be in the swampland, not in the landscape. Similarly a UV cutoff $Λ=gM_p/\sqrt{N}$ is conjectured for the U(1) gauge theory with $N$ species.
This article gives an overview of many of the recent developments in understanding the structure of relativistic scattering amplitudes in gauge theories ranging from QCD to N=4 super-Yang-Mills theory, as well as (super)gravity. I also provide a pedagogical introduction to some of the basic tools used to organize and illuminate the color and kinematic structure of amplitudes. This article is an invited review introducing a special issue of Journal of Physics A devoted to "Scattering Amplitudes in Gauge Theories".
We consider unitarity and causality in a higher-derivative theory of infinite order, where propagators fall off more quickly in the ultraviolet due to the presence of a transcendental entire function of the momentum. Like Lee-Wick theories, these field theories might provide new avenues for addressing the hierarchy problem; unlike Lee-Wick theories, tree-level propagators do not have additional poles corresponding to unobserved particles with unusual properties. We consider microscopic acausality in these nonlocal theories. The acausal ordering of production and decay vertices for ordinary res…
Recently within the context of a microscopic quantum theory, the Black Hole's Quantum N-Portrait, it was shown that continuous global symmetries are compatible with quantum black hole physics. In the present paper we revise within the same framework the semi-classical black hole bound on the number of particle species N_{species}. We show that unlike the bound on global charge, the bound on species survives in the quantum picture and gives rise to a new fundamental length-scale, L_{species} = sqrt{N_{species}} L_P$, beyond which the resolution of species identities is impossible. This finding …
Causality constrains the gravitational interactions of massive higher spin particles in both AdS and flat spacetime. We explore the extent to which these constraints apply to composite particles, explaining why they do not rule out macroscopic objects or hydrogen atoms. However, we find that they do apply to glueballs and mesons in confining large $N$ gauge theories. Assuming such theories contain massive bound states of general spin, we find parametric bounds in $(3+1)$ spacetime dimensions of the form $N\lesssim \frac{M_{Pl}}{Λ_{\text{QCD}}}$ relating $N$, the QCD scale, and the Planck scale…
Effective field theories that manifest UV/IR mode mixing in such a way as to be valid for arbitrarily large volumes, can be used for gravitational, non-black hole events to be accounted for. In formulating such theories with a large number of particle species $N$, we employ constraints from the muon $g-2$, higher-dimensional operator corrections due to the required UV and IR cutoffs as well as the RG evolution in a conventional field-theoretical model in curved space. While in general our bounds on $N$ do reflect $N \simeq 10^{32}$, a bound motivated by the solution to the hierarchy problem in…
In this paper we generalize the idea of species holography to the case of Cascading DGP theories. Essence of the phenomenon is that a 4D field theory with N particle species coupled to a high-dimensional bulk gravity propagating solely a graviton becomes strongly coupled at the scale that would be the quantum gravity scale of the bulk theory if all the species were propagating in the bulk. We will see that both, crossover scales and Vainshtein scales, can be understood as holographic scales in the above sense. We confirm our results by an explicit effective field theoretic derivation of these …
We discuss higher derivative corrections to black hole entropy in theories that allow a near horizon AdS_3 x X geometry. In arbitrary theories with diffeomorphism invariance we show how to obtain the spacetime central charge in a simple way. Black hole entropy then follows from the Euclidean partition function, and we show that this gives agreement with Wald's formula. In string theory there are certain diffeomorphism anomalies that we exploit. We thereby reproduce some recent computations of corrected entropy formulas, and extend them to the nonextremal, nonsupersymetric context. Examples inc…
We set an upper bound on the gravitational cutoff in theories with exact quantum numbers of large N periodicity, such as Z_N discrete symmetries. The bound stems from black hole physics. It is similar to the bound appearing in theories with N particle species, though a priori, a large discrete symmetry does not imply a large number of species. Thus, there emerges a potentially wide class of new theories, that address the hierarchy problem by lowering the gravitational cutoff due to existence of large Z_{10^32}-type symmetries.
We investigate the universality of microscopic eigenvalue correlations for Random Matrix Theories with the global symmetries of the QCD partition function. In this article we analyze the case of real valued chiral Random Matrix Theories ($β=1$) by relating the kernel of the correlations functions for $β=1$ to the kernel of chiral Random Matrix Theories with complex matrix elements ($β= 2$), which is already known to be universal. Our proof is based on a novel asymptotic property of the skew-orthogonal polynomials: an integral over the corresponding wavefunctions oscillates about half its asymp…
We show that, within modified gravity, the non-linear nature of the field equations implies that the usual naive averaging procedure (replacing the microscopic energy-momentum by its cosmological average) is invalid. We discuss then how the averaging should be performed correctly and show that, as a consequence, at classical level the physical masses and geodesics of particles, cosmology and astrophysics in Palatini modified gravity theories are all indistinguishable from the results of general relativity plus a cosmological constant. Palatini gravity is however a different theory from general…
In two dimensions, the topological order described by $\mathbb{Z}_2$ gauge theory coupled to free or weakly interacting fermions with a nonzero spectral Chern number $ν$ is classified by $ν\; \mathrm{mod}\; 16$ as predicted by Kitaev [Ann. Phys. 321, 2 (2006)]. Here we provide a systematic and complete construction of microscopic models realizing this so-called sixteenfold way of anyon theories. These models are defined by $Γ$ matrices satisfying the Clifford algebra, enjoy a global $\mathrm{SO}(ν)$ symmetry, and live on either square or honeycomb lattices depending on the parity of $ν$. We sh…
We note that in extensions of the Standard Model that allow for a varying fine structure constant, alpha, all matter species, apart from right-handed neutrinos, will gain an intrinsic electric dipole moment (EDM). In a large subset of varying-alpha theories, all such particle species will also gain an effective electric charge. This charge will in general not be quantised and can result in macroscopic non-conservation of electric charge.
In this paper we show how to compute the shear relaxation time from an underlying microscopic theory. We prove that the shear relaxation time in Israel-Stewart-type theories is given by the inverse of the pole of the corresponding retarded Green's function, which is nearest to the origin in the complex energy plane. Consequently, the relaxation time in such theories is a microscopic, and not a macroscopic, i.e., fluid-dynamical time scale.
We review various aspects of classical solutions in string theories. Emphasis is placed on their supersymmetry properties, their special roles in string dualities and microscopic interpretations. Topics include black hole solutions in string theories on tori and N=2 supergravity theories; p-branes; microscopic interpretation of black hole entropy. We also review aspects of dualities and BPS states.
We consider the hydrodynamics of relativistic conformal field theories at finite temperature. We show that the limit of slow motions of the ideal hydrodynamics leads to the non-relativistic incompressible Euler equation. For viscous hydrodynamics we show that the limit of slow motions leads to the non-relativistic incompressible Navier-Stokes equation. We explain the physical reasons for the reduction and discuss the implications. We propose that conformal field theories provide a fundamental microscopic viewpoint of the equations and the dynamics governed by them.
In theories with a large number N of particle species, black hole physics imposes an upper bound on the mass of the species equal to M_{Planck}/\sqrt{N}. This bound suggests a novel solution to the hierarchy problem in which there are N \approx 10^{32} gravitationally coupled species, for example 10^{32} copies of the Standard Model. The black hole bound forces them to be at the weak scale, hence providing a stable hierarchy. We present various arguments, that in such theories the effective gravitational cutoff is reduced to Λ_G \approx M_{Planck}/\sqrt{N} and a new description is needed aroun…
We consider generic derivative corrections to the Einstein gravity and find new classes of theories without ghost around the Minkowski background by means of an extension of the spacetime geometry. We assume the Riemann-Cartan geometry, i.e. a geometry with a non-vanishing torsion, and consider all possible terms in the Lagrangian up to scaling dimension four. We first clarify the number, spins, and parities of all particle species around the Minkowski background and find that some of those particle species are ghosts for generic choices of parameters. For special choices of the parameters, on…
Field theories with anisotropic scaling in 1+1 dimensions are considered. It is shown that the isomorphism between Lifshitz algebras with dynamical exponents z and 1/z naturally leads to a duality between low and high temperature regimes. Assuming the existence of gap in the spectrum, this duality allows to obtain a precise formula for the asymptotic growth of the number of states with a fixed energy which depends on z and the energy of the ground state, and reduces to the Cardy formula for z=1. The holographic realization of the duality can be naturally inferred from the fact that Euclidean L…
We revisit 2D $\mathcal{N}=(2,2)$ super Yang-Mills lattice formulation (Sugino model) to investigate its fermion action with two (Majorana) fermion flavors and exact chiral-$U(1)_{R}$ symmetry. We show that the reconcilement of chiral symmetry and absence of further species-doubling originates in the 4D clifford algebra structure of the action, where 2D two flavors are spuriously treated as a single 4D four-spinor with four 4D gamma matrices introduced into kinetic and Wilson terms. This fermion construction based on the higher-dimensional clifford algebra is extended to four dimensions in two…
Using the fact that theories of gravity with asymptotically three-dimensional anti-de Sitter geometries have dual descriptions as two-dimensional conformal field theories (CFTs), we present the first study in field theory of the thermodynamic volume of various black hole solutions. We explain in general two-dimensional CFT terms why the presence of a thermodynamic volume can render certain black hole solutions "super-entropic". Super-entropicity simply results from the fact that the Cardy formula, which gives the gravitational Bekenstein-Hawking entropy, can over-count the CFT entropy. The exa…
We consider ensemble averaged theories with discrete random variables. We propose a suitable measure to do the ensemble average. We also provide a mathematical description of such ensemble averages of theories in terms of Poisson point processes. Moreover, we demonstrate that averaging theories of this type has an equivalent description as tracing over parts of the microscopic degrees of freedom in a suitable continuous limit of a single microscopic theory. The results from both approaches can be identified with Liouville gravity, of which we further address some implications on the microscopi…
We study large families of theories of interacting spin 2 particles from the point of view of causality. Although it is often stated that there is a unique Lorentz invariant effective theory of massless spin 2, namely general relativity, other theories that utilize higher derivative interactions do in fact exist. These theories are distinct from general relativity, as they permit any number of species of spin 2 particles, are described by a much larger set of parameters, and are not constrained to satisfy the equivalence principle. We consider the leading spin 2 couplings to scalars, fermions,…
The microscopic description of AdS space obeys the holographic principle in the sense that the number of microscopic degrees of freedom is given by the area of the holographic boundary. We assume the same applies to the microscopic holographic theories for non-AdS spacetimes, specifically for Minkowski, de Sitter, and AdS below its curvature radius. By taking general lessons from AdS/CFT we derive the cut-off energy of the holographic theories for these non-AdS geometries. Contrary to AdS/CFT, the excitation energy decreases towards the IR in the bulk, which is related to the negative specific…
We continue our study of factorizing theories of dilaton gravity, characterized by a universal bilocal interaction. All such factorizing theories can be shown to have discrete spectra, distinguished only by their local dilaton potentials. We show how such theories can be used to construct all alpha-states in the Hilbert space of baby universes of ordinary JT gravity. Large classes of these theories with different local potentials are found to be non-perturbatively equivalent and have identical discrete spectra. This is a concrete example of how different bulk descriptions can give rise to the …
I show that the principle of equipartition, applied to area elements of a surface which are in equilibrium at the local Davies-Unruh temperature, allows one to determine the surface number density of the microscopic spacetime degrees of freedom in any diffeomorphism invariant theory of gravity. The entropy associated with these degrees of freedom matches with the Wald entropy for the theory. This result also allows one to attribute an entropy density to the spacetime in a natural manner. The field equations of the theory can then be obtained by extremising this entropy. Moreover, when the micr…
We study modified theories of gravity of the f(R) type in Palatini formalism. For a generic f(R) lagrangian, we show that the metric can be solved as the product of a scalar function times a rank-two tensor (or auxiliary metric). The scalar function is sensitive to the local energy-momentum density. The auxiliary metric satisfies a set of equations very similar to Einstein's equations and, for weak sources, it can be approximated by the Minkowski metric. According to this, the metric coupled to the matter strongly departs from the Minkowskian one in the neighbourhood of any microscopic physica…
