1. Ioan MunteanIndiana University-Purdue University, Fort Wayne&University of Notre Damehttp://imuntean.net1

2. Motivations for this talkI. Assert the role and importance of principles in quantumgravity (esp. in string theory)II. Endorse the model-based interpretation of stringtheory.III. Discuss the relation between dualities, unificationand ontological fundamentalism2 3. Some proposalsIII. Dualities as relations among modelsA duality principle is a general conjecture aboutrelations among string models3 4. Prospective resultsDuality and unification: Dualities are weaker than unification.Albeit not unificatory or explanatory in nature, dualities can:AccommodateIntegratePredicttheoretical facts about the dual model.Duality is not a consequence or a condition of unificationDeflationary result: Perhaps dualities are consequences of otherassumptions, such as supersymmetryDualities and structure: Dualities may unveil a deeper structure,with or without a deeper theory. (Rickles)Duality and (reductive) fundamentalism in string theory areinconsistent4 5. What is a principle in physics?Several possible answers. Philosophers envisaged principles as:a) meta-laws (Lange)b) constraints on physical models of a theoryc) methodological maximsd) as axioms (of an axiomatized system, e.g. classical mechanics. Carnap)e) as correspondences between the abstract mathematical formalism and theconcrete empirical phenomena (Reichenbach)f) Bold conjectures, but which are not proven to be falseAlthough all a)-f ) are germane to physics, I take here f ) as the mostrepresentative for quantum gravity.All in all, principles play a foundational role in the development andadvancement of a theoretical disciplineQ: In what does lie the foundation of a theory T?A: The principles that ground it.5 6. Three philosophical stancesHow do principles ground a theory?A Principle monism: a theory T should be grounded inone principle PB Principle pluralism: a theory T is grounded in anumber of independent principles {P1.Pn}C Principle deflationism: grounding a theory oneprinciple, in certain set of principles, in a completelydifferent set, or in no principle at all is a matter ofchoice.I will focus on B here.6 7. A. From the ideal to realityB. Greene (1999): Is string theory itself an inevitable consequence of some broaderprinciplepossibly but not necessarily a symmetry principlein much the same waythat the equivalence principle inexorably leads to general relativity or that gaugesymmetries lead to the nongravitational forces?String theory is missing a core principle and string theorists are all in a positionanalogous to an Einstein bereft of the equivalence principle (Greene, 1999, p. 171).there is [] no guarantee that such a fundamental principle exists, but the evolution ofphysics during the last hundred years encourages string theorists to have high hopes thatit does.L. Smolin (2002, 149) string theory in its present form most likely has the samerelationship to its ultimate form as Kepler's astronomy had to Newton's physics".The ideal: one symmetry principle may become The principle of quantum gravitySome candidates:the holographic principle `t Hooft (1993); Susskind (1995); Susskind & Lindesay (2004).The duality principle7 8. Principle monism and unificationGreene (2011, p. 82): a theory based on vibratingfilaments might not seem to have much in commonwith general relativitys curved spacetime picture ofgravity. Nevertheless, apply string theorysmathematics to a situation where gravity matters butquantum mechanics doesnt [] and out pop Einsteinsequations. Vibrating filaments and point particles arealso quite different. But apply string theorysmathematics to a situation where quantum mechanicsmatters but gravity doesnt [] and the math of stringtheory morphs into the math of quantum field theory.8 9. C. Conventionalism and principlesAny theory T can be grounded in a set of principles,but one can freely choose what set of conjecturesconstitutes the principles and what are mereconsequencesExample: the history of General Relativity.You can reformulate GR with no principle at all.The independent principles that ground a theory canchange dramatically in time.Compare and contrast: a system in logic where we caninterchange axioms with theorems and still get thesame expressiveness of the system9 10. B. Principle pluralism and problemsThe most obvious problem for the pluralist is the consistency ofprinciples.Other less dramatic is completeness and independenceTypical clash of principles in quantum gravity: principles of relativity(e.g. equivalence principle) and principles of quantum theory(superposition)Enticing results:Quantum backreaction as a logical result (inconsistency)The Weinberg-Witten (1980) theoremSemi-classical models of system are not coherent (Peres&Terno 2001)Typical solution: create a new theory with new principle(s) thatexplain(s) gravitation as a low energy limit of the new theory.Non-typical solution: postulate dualities that would relate classical andquantum regimes of different models.10 11. First claim of this presentationDualities do alleviate such a clash of principlesbetween theoriesDualities are conceptually weaker than unification, butcan replace the unificatory power when unification issimply a bridge too far11 12. What is a duality?Dualities can be both underestimated and overestimated.Trivial dualities are simply notational variantsGermane dualities are inter-theoretical relationsClaim: they are very rich philosophically but understudied inphilosophy.Notable exceptions: E. Castellani (2009), J. Cushing (1990), Muntean(2013), D. Rickles (2009, 2011, 2013)There are several dualities in classical EM and in QFT.A duality relates two theories (or models) such that:i. One theory is more classical than the other (viz. more quantum)ii. One theory is better known than the otheriii. One theory has a better explanation / prediction than the otheriv. One theory is weakly coupled, the other is strongly coupled12 13. Triviality and non-trivialityDualities can relate two completely different theories of the samephysical systemOr two completely different systems described by two different theoriesThe classical and the quantum description of the same systemA classical system to an another, quantum systemA gauge theory to a gravitational theoryA string theory to another string theoryThe weak coupling regime of a theory to its strong regimeNote: Mathematical dualities or logical dualities are only remotelyrelated to oursEquivalence between the category of sets and the category of completeatomic Boolean algebras.Conjunction and disjunction are dual13 14. A classical dualityA dual theory is obtained by a dualitytransformation:ur ur ur urE B;BEIt is a rotation duality in the complex vector field E+iBIn QED, this symmetry signals the existence ofmagnetic monopoles (g). They attract each other witha force of greater than the force between twoelectronsDuality explanation: If there are magnetic poles, theelectric charge is quantized, because: eg = 2n;1422137 15. Lessons for MaxwellThe dual invariance of the classical EM theory.ur ur urIf we define E=then Maxwell equations are:EAnd they are invariant to these transformationHere the conserved charge is:ur urE = E=15 E iB0ic t urururEEia e( ) ia q ig e q ig 16. Duality and explanationFrom the dual invariance of EM, Dirac (1931) inferred:1. The quantization of electrical charge from2. The existence of magnetic monopoles1 is a strong result. It could not be explained by other means(except by a 5D compactification mechanism, Klein 1926)The other option is to take 1 as a brute fact of the universe16qg 2 mh 17. Bosonization of fermions in 1DFor some range of the coupling constant, bosons aremore useful as fundamental particle than fermionsFor some range of constants, fermions arefundamental.By turning the couple constants, one becomes morefundamental than the other.Does this show a common structure?17 18. E-M duality and unificationThe dual invariance is strongly related to unificationThe 4-vector unifies the E and B fields.There is a deeper structure than what ordinary Maxwellequations unveilMaxwell equations are very rich in symmetries and consequentlyin dualities (compare to general relativity)Bianchi identityGauge transformationConformal symmetries (Baterman Cunningham 1909)Dual invarianceOther types of symmetries NOT present in EM:DiffeomorphismSupersymmetry (SUSY)18 F 19. The E/M duality in particleparlanceEM duality relates weak and strong coupling of the same theory.In one regime, 1, the poles are fundamental and charges are heavy and rich.Charges are heavierMonopoles are more elementaryEither the charge is elementary and the poles are composite, OR the poles areelementary and charges are composite.At =1 there is no fundamentality strictly speaking.All depends on the coupling constant .See a philosophical discussion in Castellani 2009, Rickles 2011.19 20. E-M duality in QFTThe EM duality as explained before does not survive quantization,but new dualities ariseMontonen&Olive (1977): At different coupling constants, electricand magnetic charges exchange roles.20Magnetic charge =topological charge Noetherian chargeThe magnetic monopoles =solitonsMagnetic monopoles =elementarygauge fields = elementaryparticlesGauge fields=solitonsWeak StrongStrong Weak 21. Perturbative string theoryThe perturbative formulation of string theorycontains the highest number of idealizations:strings are weakly coupled,the number of strings is relatively small andstrings vibrate against a flat, fixed backgroundspacetime (background dependence).The interaction term is a perturbation of the non-interactivedynamicsAll are problematic idealizations, but the third is themost outrageous and infamous.21 22. Background dependence as themajor drawback of string theoryin general, string theory, and other background-dependentapproaches, are [] examples of how not to go aboutconstructing a theory of quantum gravity (Rickles French 2006)background independence and structuralism are well-matchedbedfellowsCan we interpret string theory as a structural metaphysics even ifit is not (yet) background independent?Alternatives:talk about the promises of a background independent string theoryThe concept of background independence needs morephilosophical work.Dualities may play the central role of smooting out some of theseconsequences of the idealizations22 23. Whacked by the GR communityWhat is very frustrating is that [] string theory doesnot seem to fully incorporate the basic lesson of GR,which is that space and time are dynamical rather thanfixed, and relational rather than absolute [] all thathappens is that some strings move against this fixedbackground and interact with one another. (Smolin2001, 159)Penrose, Stachel, Woit and others would agree.But QFT is doing the same (basically)23 24. Non-perturbative string theoryA more realistic model of strings would assume:strings interactstring that can split and join (create/annihilate strings)They have enough energy to interact with spacetimeitself.In the strong coupling regime, the backreaction withspacetime is assumed and the background is notanymore fixed.24 25. A nave solution to backgroundindependenceCurved spacetime is reducible to a collection ofgravitonsGiven the Witten-Weinberg (no-go result), gravitonscannot be reduced to any known bosons,gravitation is simply not yet another quantum fieldtheoryTherefore you need something like strings.As gravitons are states of strings, the covariant part ofthe M space in string theory is in itself dynamical.25 26. Four interpretations[1] A collection of theories, most likely all being aspects of a morefundamental theory (M-theory"), which is ultimately the theory ofeverything (TOE) of our reality. Other theories in physics can beultimately reduced to the TOE.[2] A collection of mathematical models of strings and branes vibratingin various types of spaces, having different symmetries and properties.These string models represent aspects of known interactions inphysics: gravitation, gauge theories, black holes, etc.[3] A collection of conjectures about the relations among the stringmodels. Some of these string models may (or may not) represent realinteractions in the world;[4] A collection of conjectures about the relations between stringmodels (as in [2]) and other theories in physics: gauge theories,gravitation, black hole thermodynamics, information theory, etc.I have some reasons to adopt [3] here and to keep an eye on [4]26 27. String theoriesTypeSpacetimedimensionsSUSYgeneratorschiral open stringsheteroticcompactificationgauge group tachyonBosonic(closed)26 N = 0 no no no none yesBosonic(open)26 N = 0 no yes no U(1) yesI 10 N = (1,0) yes yes no SO(32) noIIA 10 N = (1,1) no no no U(1) noIIB 10 N = (2,0) yes no no none noHO 10 N = (1,0) yes no yes SO(32) noHE 10 N = (1,0) yes no yes E8 E8 noM-theory ? 11 N = 1 no no no none no27 28. Five string modelsThere are some relevant string models in D=101. I: SUSY, open and closed strings, group symmetry SO(32)2. IIA: SUSY, open and closed strings, non-chiral fermions. D-branes are theboundaries of open strings3. IIB: SUSY, open and closed strings, chiral fermions. D-branes are theboundaries of open strings4. Type II:5. HO: Heterotic model: SUSY, closed strings only, right moving strings andleft moving strings differ, symmetry group SO(32)6. HE: Heterotic model: SUSY, as above, but symmetry group is E8xE8Dualities:1/4: I and HO2/5: IIA and HEWittens conjecture (1995): all string models are related to each other bydualities.28 29. Interpretation of string models1 Empiricist: If this string model were true, whatphysics would look like?2. What are the realist commitments of these models?29 30. DualitiesDualities are not:Approximations of a theory by another theoryCorrespondences (as in theory correspondence)Notation variants of the same theoryIt is not (always) a symptom of a gauge freedomButThere is representational ambiguity in dualitiesDualities can highlight which features of our ontologicalpicture are not fundamental. (Rickles 2011) andThey may or may not point towards a deeper structureCan be related to the symmetries of a theoryHence their importance to underdetermination and scientificrealism30 31. A definition of dualities (Vafa)A theory is characterized by a moduli space M of thecoupling constantsIn this space we have several regions conventionallydesignated as weak coupling and strong coupling.A physical system can be represented in various places ofthe moduli space with various observables:Q[M,O ] Two physical systems Q and Q are dual if:M M ';O O ' i.e. there is an isomorphism between their moduli spacesand another between their observables31 32. Duality symmetriesIn string theory, the moduli space is very rich. Each model ischaracterized by a moduli space formed by the constants of thetheory.The string coupling constant gsThe topology of the manifoldOther fields in the backgroundEverything (?)The flow of theories is important but more complicated than in QFTIn this moduli space a duality symmetry can relate:The weak coupling region of T1 with the strong coupling region of T2The weak coupling region of T to the weak coupling region of the sameTInterchange elementary quanta with solitons (collective excitations)Exchange what is fundamental with what is composite32 33. Some known dualities33 34. S-duality, informallygs is the coupling constant in string theory. But in string theorygs is a field, has its equation, changes from place to placeA string can split into two strings. The probability if this processis gs.The D0-brane and strings can interchange the role offundamental entity.When gs is small f-strings are fundamental, light, hard to split.D0-branes or D-1 are complicated and heavy. Their excitationsare the particles (photons, gravitons)When D0 branes are light, f-string are heavierWhen gs=1 , f-strings and D-branes look the same.And topology is part of the moduli space. We can changedimensionality or topology as we walk in the moduli space.See (Sen 2002) for details34 35. T-dualitiesT1 and T2 can be different (different symmetries,gauge invariants, topologies), or can be the sametheory (self-duality)!Weak WeakT1 T235 36. A standard S-duality mapThis is not a self-duality.T1 and T2 are structurally different (differentsymmetries, gauge invariants, topologies)They can be string models or other models in QCDetc.Weak WeakT1 T2StrongStrong36 37. Rickles on dualities and unificationRickles 2011: the dualities point to the fact that thefive consistent superstring theories, that were believedto be distinct entities, are better understood asdifferent perturbative expansions of some single,deeper theory. (aka M-theory)For Rickles and some string enthusiasts, the five pointsin moduli space are representations of a single M-theory.This is the received view in the community.But.37 38. Dualities without unificationHe admits that the duality relationships between thepoints in moduli space will hold independently of theexistence of an M-theory Rickles 2012in order to achieve a computable scheme for the whole ofthe moduli space (including regions away from thedistinguished 'perturbation-friendly' points) such anunderlying theory is required Rickles 2011, my emphasisMy argument is that we do not need M-theory to see thedeep structure of the S-dualitiesOne on my assumptions is to analyze these as models, notas theoriesConceptually I separate the discussion on dualities fromthe discussion on unification38 39. Non-perturbative string theory andS-dualityIf we knew how to relate the weak coupling to thestrong coupling we would relate the non-perturbativephysics to the perturbative physics.In the ADS/CFT duality this is the path to abackground independent theory.39 40. Dual nature of duality andconclusionsWe use the weak coupling sector as a calculation device,but we trust the strong coupling sector in respect of itsontology and its structureIf duality is isomorphic there is no remainder in the dualstrong sector that cannot be explained away from the weakcoupling sectorIf we take dualities seriously we may need to investigate anew type of explanation based on dualities.We may want to take a throughout look at string modelsrelated to dualities (and not to string theories)40 41. AdS/CFT dualityWe start from a IIB theory (D=10, SUSY with N=4, openand closed strings)(Maldacena 1998) but esp (Klebanov 2002)This theory has a 16 supersymmetric group, the smallestalgebra in D=10.We take Nc parallel D3-branes close one to the other.If Ncgs 1, the low coupling regime, closed strings live inempty space and the open strings end on the D-branes anddescribe excitations of the D-branes.Open and closed strings are decoupled from eachother.41 42. Strong coupling and the YMWhen Ncgs 1 the gravitational effect of the D-braneson the spacetime metric is important, leading to acurved geometry and to a black brane.But near the horizon the strings are redshifted andhave low energy.Gauge theory exists and the physics on the D-branes isnothing else than a gauge theoryThe physics is now described by a Yang-Mills CFT withgYM=4gs42 43. Maldacenas duality conjectureThe 4D, N=4 SUSY SU(Nc) gauge theory (Yang Mills)is dual to a IIB string theory with the AdS/CFTboundary.43 44. Polchinski on branesWe start with strings in a flat background and discover that amassless closed string state corresponds to fluctuations of thegeometry. Here we found first a flat hyperplane, and thendiscovered that a certain open string state corresponds tofluctuations of its shape. We should not be surprised that thehyperplane has become dynamical.Thus the hyperplane is indeed a dynamical object, a Dirichletmembrane, or D-brane for short. The p-dimensional D-brane,from dualizing 25-p dimensions, is a Dp-brane. In thisterminology, the original U(n) open string theory contains nD25-branes.A D25-brane fills space, so the string endpoint can be anywhere:it just corresponds to an ordinary Chan-Paton factor.44 45. Current research (post 2003)People try to falsify the AdS/CFT. No success yetMore opportunistically, others try to understand blackholes through the duality as hot gases of fermionsOthers try to look for more realistic dualities:dS/CFTDualities with no SUSY, but with holographic principle(T. Banks).Understand hadrons with the IIB theory (theboomerang kid)45 46. Explanation/unification/predictionin AdS/CFT?Explanation? I do not see itUnification? Not directly, without the M-theory.Prediction? Perhaps, if we relate it to the HiggsmechanismComputational advantages? Yes, definitely!Is the holographic principle doing anyexplanatory/unification/predictive work?46 47. Emergence in string theoryDuality, when correctly interpreted, may illuminate the classical-quantum relationPeople believe spacetime emerges in AdS/CFT (Seiberg, Koch Murugan)In S-duality the non-perturbative aspects emerge from the perturbative aspects but wecompute in the perturbative sector.Some believe the curved spacetime of general relativity is a holographic emergentconstruct from a quantum gauge field without gravity rather than a fundamental featureof reality.Strong emergenceAny spacetime emerges from any gauge theoryWeak emergence:A special type of spacetime (the IIB gravitation) emerges from a special type of gaugetheory (SUSY YM in D=4)Witness we assume here that:If a theory does not have general covariance, then the theory lacks an underlyingspacetime47 48. Deflationism: ex SUSY quodlibetsequiturSUSY can be a great candidate for the deeper structureunderlying S-dualities and the AdS/CFT duality.SUGR is also present in the string sectorThis is a an argument from symmetryThere are dS/CFT dualities but no non-SUSY dualities.SUSY is part of the CFT Yang-Mills story because it isthe limit of a IIB theory.I am not pluralist about SUSY, but I ampluralist/functionalist about spacetime (andbackground independence)48 49. But symmetry is not enough inAdS/CFTIn AdS/CFT we do not have a symmetry in the modulispace.It is not like a gauge orbifold in the moduli spaceThere is something else than symmetry here.49 50. ReferencesBousso, R. (2002). The holographic principle. Reviews of Modern Physics, 74(3), 825874.doi:10.1103/RevModPhys.74.825Bueno, O., French, S., & Ladyman, J. (2002). On Representing the Relationship between theMathematical and the Empirical. Philosophy of Science, 69(3), 497518.Callender, C., & Huggett, N. (2001). 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