Ioan Muntean Indiana University-Purdue University,

Fort Wayne, Indiana, USA http://imuntean.net

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Motivations for this talk I. Underdetermination II. Unification and explanation

Do structures unify? Do they explain? III. Fundamentalism IV. Emergence of spacetime structures In this talk I will focus especially on II-IV, but add: Dualities

Does duality unveil a “deeper structure” beyond the two theories? What is a structure?

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Assumptions of my argument A. “String theory” is a collection of mathematical

models, not a theory (or a collection of theories) B. Dualities play a role in the structural interpretation

of string theory C. Reality and structures are not scale invariant.

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Prospective results D. Dualities are not unificatory or explanatory (pace

Rickles) E. Dualities unveil a deeper structure, with or without

a deeper theory. F. Dualities act as corrective relations to string models.

They may predict and accommodate/integrate facts about the dual model.

I take accommodation / integration as weaker than unification and explanation. 4

A. String Theory as a quantum gravity program String theory:

Is a “particle physics” programme (cf. a “relativity” programme )

Uses additional structures: supersymmetry, geometrical objects (branes), unnatural fields (“the dilaton”)

It is mainly perturbative, although a non-perturbative formulation is sought for

(French, Rickles 2006)

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Structural realism and string theory Quantum gravity is a natural framework to discuss structural realism (Rickles,

French Saatsi, 2006); (Rickles 2010, 2011, 2012). a metaphysics of relations is suggested by quantum gravity (Smolin, Baez) This relationalism is easily and best construed as a variety of structuralism

(French, Rickles 2006) String theory is a “main contender” in the search for quantum gravity

Does it reveal relationism? Or structuralism? String theory is a quantum field program

hence its benefits and sins : although it solves UV divergences, it is background dependent

String theory is an ever-changing, paradigm-shifting, self-inventing “theory” It constitutes a good playground for ESR

It is natural to investigate “a the structural interpretation of string theory”.

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Structural realism and background dependence “in general, string theory, and other background-dependent

approaches, are […] examples of how not to go about constructing a theory of quantum gravity” (Rickles French 2006)

background independence and structuralism are “well-matched bedfellows”

Can we interpret string theory as a structural metaphysics even if it is not (yet) background independent?

Alternatives: talk about the promises of a background independent string theory The concept of background independence needs more

philosophical work. Dualities may play the central role

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Spanked by the GR community “What is very frustrating is that […] string theory does

not seem to fully incorporate the basic lesson of GR, which is that space and time are dynamical rather than fixed, and relational rather than absolute […] all that happens is that some strings move against this fixed background and interact with one another.” (Smolin 2001, 159)

Penrose, Stachel, Woit and others would agree.

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String Theory and spacetime String models depend on a background Unlike other QG programs, in ST the structure of

spacetime is more complicated: Dimensionality D>4 Exotic topologies Compactification The dynamics of spacetime is codified by the “dilaton”

field The GR physicists would insist:

So what? What determines the structure of the convoluted spacetime?

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The naïve solution Curved spacetime is reducible to a collection of

gravitons Given the Witten-Weiberg (no-go result), gravitons

cannot be reduced to any known bosons, gravitation is simply not “yet another quantum field

theory” Therefore you need something like strings. As gravitons are states of strings, the covariant part of

the M space in string theory is in itself dynamical.

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Four interpretations [1] A collection of theories in quantum gravity, all being aspects of

a more fundamental theory (“M-theory”) which is ultimately the theory of everything (TOE) of our reality. Other theories in physics can/will be reduced to the TOE.

[2] string theory is a model of different aspects of reality. Most plausibly, string theory is a model of Hadrons.

[3] A collection of string models which are mathematical models of strings and branes vibrating in various types of spaces, having different symmetries and geometries.

[4] A collection of conjectures about the relations among the string models (interpreted as in [3])

[5] A collection of conjectures about the relations between string models (as in [3]) and other theories in physics: gauge theories, gravitation, thermodynamics of black hole, information theory, etc.

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What is the perturbative approach? An idealization As in “a collection of models” some based on this

idealization, some presumably not.

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Five string models There are five string models of interest in D=10 1. I: SUSY, open and closed strings, group symmetry SO(32) 2. IIA: SUSY, open and closed strings, non-chiral fermions. D-branes

are the boundaries of open strings 3. IIB: SUSY, open and closed strings, chiral fermions. D-branes are the

boundaries of open strings 4. HO: Heterotic model: SUSY, closed strings only, right moving strings

and left moving strings differ, symmetry group SO(32) 5. HE: Heterotic model: SUSY, as above, but symmetry group is E8xE8

Dualities:

1/4: I and HO 2/5: IIA and HE

Witten’s conjecture (1995): all string models are related to each other by dualities.

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B. Interpretation of string models 1 Empiricist: If this string model were true, what

physics would look like? 2. What are the realist commitments of these models?

I choose here 2.

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Structural questions about string models

Is string theory object-oriented? If not, what plays the role of the structure? What is fundamental? What is non-fundamental? Is the structural interpretation better off than object

oriented interpretations? They need to be addressed within each string model.

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Object-oriented string realism Strings are fundamental entities They are objects, not structures They have 2D features, not intrinsic properties as

particles They have individuation and individuality Their excitations are other particles (gravitons,

photons, some gluons etc.) Therefore the individuation of particles depends on

the individuation of strings.

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Against the OO string realism “Acceptable in the 80s” perhaps Now we are past the brane revolution Branes are as fundamental as strings Are branes objects?

No, they are structures Yes, they are.

Strings are “‘intersections’ of branes” cf Cassirer: “electrons are points of intersection”

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D-branes “We start with strings in a flat background and discover that a

massless closed string state corresponds to fluctuations of the geometry. Here we found first a flat hyperplane, and then discovered that a certain open string state corresponds to fluctuations of its shape. We should not be surprised that the hyperplane has become dynamical.”

“Thus the hyperplane is indeed a dynamical object, a Dirichlet membrane, or D-brane for short. The p-dimensional D-brane, from dualizing 25-p dimensions, is a Dp-brane. In this terminology, the original U(n) open string theory contains n D25-branes.”

A D25-brane fills space, so the string endpoint can be anywhere: it just corresponds to an ordinary Chan-Paton factor.

Polchinski, vol I, 269

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Dualities symmetries and their interpretations Dualities are present in logic, mathematics, physics In general, they are not philosophically appealing Should structural realists pay more attention to dualities? Some dualities for philosophers:

E/M duality (Castellani 2009, Rickles 2011,2012) Bosonization of fermions in 1D s-channel/t-channel duality of the dual model of hadrons S-dualities in string theory AdS/CFT duality

My claim is that the structural realist should pay attention to some of these.

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Dualities Dualities are not:

Approximations of a theory by another theory Correspondences (as in “theory correspondence”) Notation variants of the same theory It is not (always) a symptom of a gauge freedom

But There is representational ambiguity in dualities “Dualities can highlight which features of our ontological

picture are not fundamental”. Rickles 2011 Can be related to the symmetries of a theory Hence their importance to underdetermination and scientific

realism

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A definition of dualities (Vafa) A theory is characterized by a moduli space M of the

coupling constants In this space we have several regions conventionally

designated as weak coupling and strong coupling. A physical system can be represented in various places of

the moduli space with various observables:

Two physical systems Q and Q’ are dual if:

i.e. there is an isomorphism between their moduli spaces and one between their observables

[ , ]Q M Oα

'; 'M M O Oα α↔ ↔

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Triviality and non-triviality Dualities can relate two completely different theories of the same

physical system Or two completely different systems described by two different

theories The classical and the quantum theory of a system A classical system to a quantum system A gauge theory to a gravitational theory A string theory to another string theory The weak coupling regime of a theory to its strong regime Claims in this talk:

some dualities are not philosophically trivial, Some dualities in string theory are important to the structural

interpretation of quantum gravity

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E/M duality (Dirac) A dual theory is obtained by a “duality

transformation”:

It is a rotation duality in the complex vector field E+iB In QED, this symmetry signals the existence of

magnetic monopoles (g). They attract each other with a force of (2/137)^2 greater than the force between two electrons

Duality explanation: If there are magnetic poles, the electric charge is quantized, because: eg = 2n;

;E B B E→ →−

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The E/M duality in particle parlance EM duality relates weak and strong coupling of the same theory. In one regime, α small, the electron charge is weak, i.e. it does

not interact with its own field (fine structure constant). Electrons barely radiate photons. The electric field is weak. They are hard to excite (can we excite an electron?)

There are poles, but they have large fields around them, they are heavy. The poles are hard to separate, spread out, composite, solitonic excitations. Structurally they are very rich.

At α large, the poles are fundamental and charges are heavy and rich.

Either the charge is elementary and the poles are composite, OR the poles are elementary and charges are composite.

All depends on the coupling constant α. Castellani 2009, Rickles 2011.

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Bosonization of fermions in 1D For some range of the coupling constant, bosons are

more useful as fundamental particle than fermions For some range of constants, fermions are

fundamental. By turning the couple constants, one becomes more

fundamental than the other. Does this show a common structure? In 1+D this does not happen

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Duality symmetries In string theory, the moduli space is very rich. Each model is

characterized by a “moduli space” formed by the constants of the theory. The string coupling constant gs The topology of the manifold Other fields in the background Everything (?)

The flow of theories is important but more complicated than in QFT In this moduli space a duality symmetry can relate:

The weak coupling region of T1 with the strong coupling region of T2 The weak coupling region of T to the weak coupling region of the same

T Interchange elementary quanta with solitons (collective excitations) Exchange what is fundamental with what is composite

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S-duality, informally gs is the coupling constant in string theory. But in string theory

gs is a field, has its equation, changes from place to place A string can split into two strings. The probability if this process

is ≈ gs. The D0-brane and “strings” can interchange the role of

fundamental entity. When gs is small f-strings are fundamental, light, hard to split.

D0-branes or D-1 are complicated and heavy. Their excitations are the particles (photons, gravitons)

When D0 branes are light, f-string are heavier When gs=1 , f-strings and D-branes look the same. And topology is part of the moduli space. We can change

dimensionality or topology as we walk in the moduli space. See (Sen 2002) for details

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T-dualities T1 and T2 can be different (different symmetries,

gauge invariants, topologies), or can be the same theory (self-duality)!

T1 T2 Weak Weak

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A standard S-duality map

This is not a “self-duality”. T1 and T2 are structurally different (different

symmetries, gauge invariants, topologies) They can be string models or other models in QCD

etc.

T1 T2

Strong Strong

Weak Weak

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D. Dualities and unification Rickles 2011: “the dualities point to the fact that the

five consistent superstring theories, that were believed to be distinct entities, are better understood as different perturbative expansions of some single, deeper theory.” (aka M theory)

For Rickles, the five points in moduli space are representations of a single M-theory.

This is the received view in the community. But….

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Dualities without unification “the duality relationships between the points in moduli space

will hold independently of the existence of an M-theory” Rickles 2012

but “in order to achieve a computable scheme for the whole of the moduli space (including regions away from the distinguished 'perturbation-friendly' points) such an underlying theory is required” Rickles 2011, my emphasis

My argument is that we do not need M-theory to see the deep structure of the S-dualities

One on my assumptions is to analyze these as models, not as theories

Conceptually I separate the discussion on dualities from the discussion on unification

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Non-perturbative string theory and S-duality If we knew how to relate the weak coupling to the

strong coupling we would relate the non-perturbative physics to the perturbative physics.

In the ADS/CFT duality this is the path to a background independent theory.

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Dive in AdS/CFT duality We start from a IIB theory (D=10, SUSY with N=4, open

and closed strings) (Maldacena 1998) but esp (Klebanov 2002) This theory has a 16 supersymmetric group, the smallest

algebra in D=10. We take Nc parallel D3-branes close one to the other. If Ncgs ≪ 1, the low coupling regime, closed strings live in

empty space and the open strings end on the D-branes and describe excitations of the D-branes.

Open and closed strings are decoupled from each other.

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Strong coupling and the YM When Ncgs ≫ 1 the gravitational effect of the D-branes

on the spacetime metric is important, leading to a curved geometry and to a “black brane”.

But near the horizon the strings are redshifted and have low energy.

Gauge theory exists and the physics on the D-branes is nothing else than a gauge theory

The physics is now described by a Yang-Mills CFT with gYM=4πgs

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Maldacena’s duality conjecture The 4D, N=4 SUSY SU(Nc) gauge theory (Yang Mills)

is dual to a IIB string theory with the AdS/CFT boundary.

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Current research (post 2003) People try to falsify the AdS/CFT. No success yet More opportunistically, others try to understand black

holes through the duality as hot gases of fermions Others try to look for more realistic dualities:

dS/CFT Dualities with no SUSY, but with holographic principle

(T. Banks). Understand hadrons with the IIB theory (“the

boomerang kid”)

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E. The structure in the AdS/CFT 1. Is the Yang-Mills CFT the hidden structure of a string IIB

theory (which has gravitation in it)? 2. Is string structure of IIB model the hidden structure of the

Yang-Mills CFT? 3. Are they both aspects of a hidden structure?

A. M theory B. SUSY C. Other hidden structural assumption

4. Or perhaps we deal here with a loopy dependence relation?

3. B, 4, 3.A., 2, 1. Physicists believe 1. In this order of preference

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Explanation/unification/prediction in AdS/CFT? Explanation? I do not see it Unification? Not directly, without the M-theory. Prediction? Perhaps, if we relate it to the Higgs

mechanism Computational advantages? Yes, definitely! Is the holographic principle doing any

explanatory/unification/predictive work?

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F. Emergence? No, accommodation! May solve the problem of emergence in this case People believe spacetime emerges in AdS/CFT (Seiberg, Koch

Murugan) Some believe the curved spacetime of general relativity is a

holographic emergent construct from a quantum gauge field without gravity rather than a fundamental feature of reality.

Strong emergence Any spacetime emerges from any gauge theory

Weak emergence: A special type of spacetime (the IIB gravitation) emerges from a

special type of gauge theory (SUSY YM in D=4) Witness we assume here that:

“If a theory does not have general covariance, then the theory lacks an underlying spacetime”

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Spacetime structuralism in AdS/CFT We ignore the bulk fapp. We focus on the boundary We achieve a sort of background independence from

the bulk Not independence on the boundary. We may be OO realist on the boundary but we do not

need to be OO realists in the bulk

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The OSR answer Weak dependence A structure of spacetime depend on a non-spacetime

structure I take the CFT YM structure as determined by SUSY.

AdS/CFT: The AdS covariance (therefore the graviton

field) depends on the gauge symmetries of CFT There is SUSY in both!!!

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Ex SUSY quodlibet sequitur SUSY can be a great candidate for the deeper structure

underlying S-dualities and the AdS/CFT duality. SUGR is also present in the string sector This is a an argument from symmetry There are dS/CFT dualities but no non-SUSY dualities. SUSY is part of the CFT Yang-Mills story because it is

the limit of a IIB theory. I am not pluralist about SUSY, but I am

pluralist/functionalist about spacetime (and background independence)

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But symmetry is not enough In AdS/CFT we do not have a symmetry in the moduli

space. It is not like a gauge orbifold in the moduli space There is something else than symmetry here.

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Back to realism? Nothing look even slightly related to reality:

SUSY? SUGR? D=10? Large NC?

BUT: In string theory spacetime is in fact a field that can be

traded with strings and branes. We can trade in NC and D=10 with other assumptions Give up the OO string realism because all these are

mathematical models

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Conclusion Dive-in in dualities Interpret them as a stay-in feature of QG They entail a decent OSR interpretation There is also some conventionalism/antirealism fronts

to fight on.

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