## Stanford's Shamit Kachru on Breaking Supersymmetry

#### Special Topic of Supersymmetry Interview, March 2012

Kachru is a professor of physics at Stanford University, and also a professor at the Stanford Linear Accelerator. |

In the interview below, Kachru speaks to ScienceWatch.com about his highly cited work pertaining to supersymmetry.

**Would you tell us a bit about your educational background and research experiences?**

I was educated at University High School in Urbana, Illinois; at Harvard (undergraduate); and at Princeton (Ph.D., under the guidance of Edward Witten). I was interested in theoretical physics and mathematics from an early age. My first serious influence in terms of modern research was Cumrun Vafa at Harvard (with whom I talked extensively as an undergraduate), and my earliest research was on string compactifications.

At that time, some of the most interesting issues revolved around studies of processes that look singular in general relativity but could be smoothed out by string theory corrections. Famous examples include topology-change in Calabi-Yau compactifications, and my first excitement in research came when we found a new way to make smooth topology-changing transitions in studies of heterotic string compactifications on Calabi-Yau spaces with non-trivial vector bundles over them. The same general sorts of models are popular today in discussions of Grand Unified Theories from string theory.

**What first drew your interest to the research area of supersymmetry?**

I think my serious interest in supersymmetry grew out of the realization that in supersymmetric theories, one could see striking evidence for highly non-trivial dualities between *a priori* very different theories. Sen gave striking evidence for strong/weak coupling duality of maximally supersymmetric Yang-Mills theory in early 1994; slightly later the same year, Seiberg and Witten used subtle and beautiful ideas to solve N=2 supersymmetric quantum field theories ("solve" in the sense of determining the low-energy effective Lagrangian, with terms up to two derivatives, very precisely as a function of moduli fields).

A few months later similar ideas began to shed light on dualities in string theory. My first serious work in the area came when I realized, with Cumrun Vafa, that heterotic and type II string compactifications on very different manifolds (the former on a K3 surface times a torus with a non-trivial vector bundle parametrising the gauge fields, the latter on a Calabi-Yau threefold) were actually exactly dual to one another, and in fact the duality was a realization of the Seiberg-Witten solution of supersymmetric gauge theory (in local neighborhoods in moduli space).

A slice through a Calabi-Yau manifold

More precisely, the heterotic theory made manifest the UV degrees of freedom (e.g., non-Abelian gauge fields), while the type II dual made manifest the low-energy solution! Combining duality with mirror symmetry, this gave us a way to "solve" N=2 compactifications of string theory. This technique was later refined to give very straightforward ways of solving N=2 theories by engineering the appropriate type II geometry.

**Your most-cited paper in our analysis is the 2003 Physical Review D paper, "de Sitter vacua in string theory."(Kachru S, et al. 68[4]: No. 046005, 2003), now cited roughly 1,300 times. Could you talk a little bit about this paper and why it has been so influential?**

The "KKLT" paper, as it’s known from the authors’ last initials, has been influential because it lies at the confluence of several fields and ideas. At the most straightforward level, it gave very concrete and extendable ideas for how to stabilize the extra scalar fields of string theory, the moduli, in so-called "flux compactifications" of string theory.

We had developed a basic picture of such compactifications in an earlier paper with Giddings and Polchinski, which was very influential in my thinking. That work sketched how to make very clean models with few remaining moduli, and the "KKLT" paper outlined ways to finish the job. The easiest constructions lead to supersymmetric AdS vacua. But it also incorporated ideas I had developed earlier with H. Verlinde on how to find models of metastable non-supersymmetric vacua; this together with the former ingredients could lead also to stable models with SUSY broken and positive as well as negative vacuum energy.

So in addition to being a step towards solving a traditional problem in old string models, it was a also a very concrete step towards making stringy models of de Sitter space (the maximally symmetric solution of gravity with positive vacuum energy). Inasmuch as a positive cosmological constant was regarded as a likely ingredient in nature starting in 1998 (after the studies of type Ia supernovae found accelerated expansion of the Universe), this was an interesting development. Such constructions could also be readily generalized to both solve old problems of inflationary model building in string theory and to suggest new classes of inflationary models; this has been a growth industry, with one of the first models (the so-called "KKLMMT" model) being suggested as a small generalization of the original paper. Lastly, because of the appearance of a small vacuum energy in nature, there have been extensive discussions of a so-called "string landscape."

The "KKLT" paper gave one of the simplest toy models illustrating why one believes such a landscape to exist. An earlier model, the Bousso-Polchinski model of the landscape, is even easier to understand, but in some sense the "KKLT" construction incorporated more of the real complications of making a fully consistent string compactification, while illustrating that many of the Bousso-Polchinski ideas still seemed likely to be robust in such a context.

"There are many new avenues to explore, with the promise of taking us beyond the SUSY playground that has dominated much of our thinking for the past 25 years."

**One of the aspects of your work is designing models of supersymmetry breaking. Would you tell us about this, and some of the key papers you have published in this area (on our list or not)?**

Here, my main focus has been to find models that illustrate new phenomena in gauge/string theory, or that address issues of UV sensitivity. With Pearson and H. Verlinde, using holography, we found metastable states in the cascading field theory studied by Klebanov and Strassler; these were some of the earliest widely studied metastable vacua in vector-like gauge theories. With Aharony and Silverstein, we proposed a new method of breaking supersymmetry that could arise in string models at a non-perturbative level, but which requires only very simple gauge groups (e.g., Abelian theories), instead of the complicated non-Abelian groups involved in typical field theory models.

And with Franco and collaborators, we found the first simple constructions of so-called "single-sector models" of supersymmetry breaking. Such models unify the hidden and observable sectors normally invoked in SUSY model building. The first two generations of standard-model matter particles are composites of the same strong sector that breaks SUSY; this can both give large soft masses to the first two generation sparticles (which is good for issues of flavor-changing neutral currents), and also explain the structure of Yukawa couplings seen in the standard model. While our constructions were rather ugly, they have been simplified and beautified to some extent by Behbahani, Craig, Torroba, and others. This kind of model building could become a growth industry if the LHC uncovers evidence of SUSY with very massive sparticles in the first two generations.

**Recently, your group published "Generalized attractor points in gauged supergravity" in Physical Review D (Kachru S, et al. 84[4]: No. 046003, 2011). Please tell us about this work.**

If I may, I'd rather discuss the more recent paper that I recently submitted with Harrison and Torroba (Harrison S, *et al.*, “A maximally supersymmetric Kondo model,” arXiv:1110.5325). This paper uses supersymmetry in a very different way than it is used in particle physics models. One of my current interests is to use techniques of supersymmetric field and string theory to shed light on strongly coupled phases of the sort that are seen in condensed matter systems. One of the central questions there involves “non-Fermi liquids," which can emerge in the low-energy physics of various metals as one tunes them through quantum critical points.

A central class of such systems, the heavy fermion metals, are thought to have behavior governed by lattices of defects interacting magnetically with the bulk metallic electrons. With Harrison and Torroba, building on earlier work with Jensen, Karch, Polchinski, Silverstein, and Yaida, we have been trying to develop ways to solve such defect problems, using SUSY as an additional constraint on the dynamics. We believe the extended supersymmetry in such constructions may give us toy models where we can prove that some of the behaviors conjectured to occur in such materials actually do occur in controlled quantum field theory examples.

**How have ideas on supersymmetry changed in the past decade? What are the primary challenges that remain to be met in the next?**

In studies of SUSY, the central revolution of the past 15 years was duality—between different supersymmetric theories, as well as between field theories and gravity. In contrast, the central revolution in this area in the next few years will definitely come from experiment! The Large Hadron Collider (LHC) is up and running now. It will either find evidence for low-energy SUSY, or give strong evidence that low-energy SUSY is irrelevant to the hierarchy problem. In the former case, this will be a triumph of human imagination; the idea of fermionic extra dimensions ("superspace") was invented abstractly in the early 1970s and was used to solve a purely theoretical problem in particle physics (the "hierarchy problem") by around 1980. Seeing that these imaginative ideas were not just self-consistent but that they also capture the behavior of nature would give us confidence in our prejudices about theoretical physics.

On the other hand, there is currently no hint of SUSY from collider or other experiments, and it could be that the LHC will give evidence for only a Higgs, for a rich non-supersymmetric spectrum of particles, or for something even less expected. In any of these cases, the central role of SUSY in theoretical physics will quickly disappear. While it will still be a tremendously useful tool for exploring dynamics of toy field theories, it will become a province of purely mathematical physicists, interesting in the same way as, for example, integrable models or exactly soluble lattice systems. I find either possibility very interesting, and just want to know the answer! After all, in the latter case, there are many new avenues to explore, with the promise of taking us beyond the SUSY playground that has dominated much of our thinking for the past 25 years.

**Dr. Shamit Kachru
Stanford University, CA**